{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook, you will implement the kinematic bicycle model. The model accepts velocity and steering rate inputs and steps through the bicycle kinematic equations. Once the model is implemented, you will provide a set of inputs to drive the bicycle in a figure 8 trajectory.\n",
    "\n",
    "The bicycle kinematics are governed by the following set of equations:\n",
    "\n",
    "\\begin{align*}\n",
    "\\dot{x}_c &= v \\cos{(\\theta + \\beta)} \\\\\n",
    "\\dot{y}_c &= v \\sin{(\\theta + \\beta)} \\\\\n",
    "\\dot{\\theta} &= \\frac{v \\cos{\\beta} \\tan{\\delta}}{L} \\\\\n",
    "\\dot{\\delta} &= \\omega \\\\\n",
    "\\beta &= \\tan^{-1}(\\frac{l_r \\tan{\\delta}}{L})\n",
    "\\end{align*}\n",
    "\n",
    "where the inputs are the bicycle speed $v$ and steering angle rate $\\omega$. The input can also directly be the steering angle $\\delta$ rather than its rate in the simplified case. The Python model will allow us both implementations.\n",
    "\n",
    "In order to create this model, it's a good idea to make use of Python class objects. This allows us to store the state variables as well as make functions for implementing the bicycle kinematics. \n",
    "\n",
    "The bicycle begins with zero initial conditions, has a maximum turning rate of 1.22 rad/s, a wheelbase length of 2m, and a length of 1.2m to its center of mass from the rear axle.\n",
    "\n",
    "From these conditions, we initialize the Python class as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from grading import BicycleSolution, grade_bicycle\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.image as mpimg\n",
    "\n",
    "class Bicycle():\n",
    "    def __init__(self):\n",
    "        self.xc = 0\n",
    "        self.yc = 0\n",
    "        self.theta = 0\n",
    "        self.delta = 0\n",
    "        self.beta = 0\n",
    "        \n",
    "        self.L = 2\n",
    "        self.lr = 1.2\n",
    "        self.w_max = 1.22\n",
    "        \n",
    "        self.sample_time = 0.01\n",
    "        \n",
    "    def reset(self):\n",
    "        self.xc = 0\n",
    "        self.yc = 0\n",
    "        self.theta = 0\n",
    "        self.delta = 0\n",
    "        self.beta = 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A sample time is required for numerical integration when propagating the kinematics through time. This is set to 10 milliseconds. We also have a reset function which sets all the state variables back to 0. \n",
    "\n",
    "With this sample time, implement the kinematic model using the function $\\textit{step}$ defined in the next cell. The function should take speed + angular rate as inputs and update the state variables. Don't forget about the maximum turn rate on the bicycle!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Bicycle(Bicycle):\n",
    "    def step(self, v, w):\n",
    "        # ==================================\n",
    "        #  Implement kinematic model here\n",
    "        # ==================================\n",
    "        xvel = v * np.cos(self.theta + self.beta)\n",
    "        yvel = v * np.sin(self.theta + self.beta)\n",
    "        thetavel = v * np.cos(self.beta) * np.tan(self.delta) / self.L\n",
    "        deltavel = min(self.w_max, max(w, -self.w_max))\n",
    "        \n",
    "        self.xc += xvel * self.sample_time\n",
    "        self.yc += yvel * self.sample_time\n",
    "        self.theta += thetavel * self.sample_time\n",
    "        self.delta += deltavel * self.sample_time\n",
    "        self.beta = np.arctan2(self.lr * np.tan(self.delta), self.L)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the model setup, we can now start giving bicycle inputs and producing trajectories. \n",
    "\n",
    "Suppose we want the model to travel a circle of radius 10 m in 20 seconds. Using the relationship between the radius of curvature and the steering angle, the desired steering angle can be computed.\n",
    "\n",
    "\\begin{align*}\n",
    "    \\tan{\\delta} &= \\frac{L}{r} \\\\\n",
    "    \\delta &= \\tan^{-1}(\\frac{L}{r}) \\\\\n",
    "           &= \\tan^{-1}(\\frac{2}{10}) \\\\\n",
    "           &= 0.1974\n",
    "\\end{align*}\n",
    "\n",
    "If the steering angle is directly set to 0.1974 using a simplied bicycled model, then the bicycle will travel in a circle without requiring any additional steering input. \n",
    "\n",
    "The desired speed can be computed from the circumference of the circle:\n",
    "\n",
    "\\begin{align*}\n",
    "    v &= \\frac{d}{t}\\\\\n",
    "     &= \\frac{2 \\pi 10}{20}\\\\\n",
    "     &= \\pi\n",
    "\\end{align*}\n",
    "\n",
    "We can now implement this in a loop to step through the model equations. We will also run our bicycle model solution along with your model to show you the expected trajectory. This will help you verify the correctness of your model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample_time = 0.01\n",
    "time_end = 20\n",
    "model = Bicycle()\n",
    "solution_model = BicycleSolution()\n",
    "\n",
    "# set delta directly\n",
    "model.delta = np.arctan(2/10)\n",
    "solution_model.delta = np.arctan(2/10)\n",
    "\n",
    "t_data = np.arange(0,time_end,sample_time)\n",
    "x_data = np.zeros_like(t_data)\n",
    "y_data = np.zeros_like(t_data)\n",
    "x_solution = np.zeros_like(t_data)\n",
    "y_solution = np.zeros_like(t_data)\n",
    "\n",
    "for i in range(t_data.shape[0]):\n",
    "    x_data[i] = model.xc\n",
    "    y_data[i] = model.yc\n",
    "    model.step(np.pi, 0)\n",
    "    \n",
    "    x_solution[i] = solution_model.xc\n",
    "    y_solution[i] = solution_model.yc\n",
    "    solution_model.step(np.pi, 0)\n",
    "    \n",
    "    #model.beta = 0\n",
    "    #solution_model.beta=0\n",
    "    \n",
    "plt.axis('equal')\n",
    "plt.plot(x_data, y_data,label='Learner Model')\n",
    "plt.plot(x_solution, y_solution,label='Solution Model')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "The plot above shows the desired circle of 10m radius. The path is slightly offset which is caused by the sideslip effects due to $\\beta$. By forcing $\\beta = 0$ through uncommenting the last line in the loop, you can see that the offset disappears and the circle becomes centered at (0,10). \n",
    "\n",
    "However, in practice the steering angle cannot be directly set and must be changed through angular rate inputs $\\omega$. The cell below corrects for this and sets angular rate inputs to generate the same circle trajectory. The speed $v$ is still maintained at $\\pi$ m/s."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0\n",
      "0.031415926535897934\n",
      "0.06283101135173091\n",
      "0.09424348168454444\n",
      "0.12565142723296957\n",
      "0.1570527953449905\n",
      "0.18844538611350123\n",
      "0.21982684737913938\n",
      "0.2511946696400745\n",
      "0.282546180868636\n",
      "0.31387854123489695\n",
      "0.3451887377375815\n",
      "0.376473578742941\n",
      "0.4077296884325478\n",
      "0.4389535011612858\n",
      "0.47014125572717846\n",
      "0.5012889895550892\n",
      "0.5323925327967545\n",
      "0.5634475023500773\n",
      "0.5944867326984626\n",
      "0.6255098900466699\n",
      "0.6565166407723075\n",
      "0.6875066514294202\n",
      "0.7184795887520752\n",
      "0.7494351196579458\n",
      "0.7803729112518939\n",
      "0.8112926308295492\n",
      "0.8421939458808877\n",
      "0.8730765240938073\n",
      "0.9039400333577015\n",
      "0.9347841417670306\n",
      "0.9656085176248916\n",
      "0.9964128294465849\n",
      "1.027196745963179\n",
      "1.0579599361250733\n",
      "1.0887020691055578\n",
      "1.119422814304371\n",
      "1.1501218413512553\n",
      "1.1807988201095094\n",
      "1.211453420679539\n",
      "1.2420853134024048\n",
      "1.2726941688633664\n",
      "1.303279657895426\n",
      "1.3338414515828683\n",
      "1.3643792212647965\n",
      "1.394892638538668\n",
      "1.4253813752638251\n",
      "1.4558451035650248\n",
      "1.4862834958359636\n",
      "1.5166962247428015\n",
      "1.5470829632276815\n",
      "1.577443384512247\n",
      "1.6077771621011567\n",
      "1.6380839697855942\n",
      "1.6683634816467774\n",
      "1.6986153720594628\n",
      "1.7288393156954474\n",
      "1.7590349875270672\n",
      "1.7892020628306926\n",
      "1.8193402171902204\n",
      "1.849449126500563\n",
      "1.879528466971133\n",
      "1.909577915129326\n",
      "1.9395971478239986\n",
      "1.9695858422289443\n",
      "1.9995436758463643\n",
      "2.0294703265103364\n",
      "2.059365472390279\n",
      "2.089228791994412\n",
      "2.1190599641732155\n",
      "2.148858668122881\n",
      "2.178624583388764\n",
      "2.208357389868828\n",
      "2.238056767817087\n",
      "2.2677223978470464\n",
      "2.297353960935135\n",
      "2.3269511384241373\n",
      "2.356513612026619\n",
      "2.386041063828351\n",
      "2.4155331762917287\n",
      "2.444989632259185\n",
      "2.4744101149566027\n",
      "2.50379430799672\n",
      "2.5331418953825335\n",
      "2.562452561510696\n",
      "2.5917259911749113\n",
      "2.6209618695693226\n",
      "2.6501598822918995\n",
      "2.6793197153478174\n",
      "2.7084410551528357\n",
      "2.737523588536669\n",
      "2.766567002746356\n",
      "2.795570985449621\n",
      "2.8245352247382356\n",
      "2.8534594091313696\n",
      "2.882343227578943\n",
      "2.9111863694649704\n",
      "2.9399885246109014\n",
      "2.9687493832789564\n",
      "2.9974686361754563\n",
      "3.0261459744541503\n",
      "3.0547810897195364\n",
      "3.0833736740301783\n",
      "3.1119234199020163\n",
      "3.1404300203116744\n",
      "3.168893168699762\n",
      "3.197312558974171\n",
      "3.225687885513367\n",
      "3.2540188431696757\n",
      "3.2823051272725654\n",
      "3.3105464336319224\n",
      "3.338742458541323\n",
      "3.3668928987812996\n",
      "3.3949974516226002\n",
      "3.4230558148294463\n",
      "3.4510676866627805\n",
      "3.479032765883513\n",
      "3.5069507517557614\n",
      "3.5348213440500835\n",
      "3.5626442430467073\n",
      "3.5904191495387527\n",
      "3.6181457648354507\n",
      "3.6458237907653546\n",
      "3.673452929679547\n",
      "3.7010328844548392\n",
      "3.7285633584969697\n",
      "3.75604405574379\n",
      "3.783474680668452\n",
      "3.8108549382825823\n",
      "3.838184534139458\n",
      "3.865463174337171\n",
      "3.89269056552179\n",
      "3.9198664148905134\n",
      "3.94699043019482\n",
      "3.9740623197436116\n",
      "4.001081792406348\n",
      "4.028048557616179\n",
      "4.054962325373071\n",
      "4.081822806246923\n",
      "4.108629711380679\n",
      "4.135382752493438\n",
      "4.162081641883549\n",
      "4.188726092431707\n",
      "4.2153158176040435\n",
      "4.2418505314552055\n",
      "4.268329948631429\n",
      "4.2947537843736106\n",
      "4.321121754520367\n",
      "4.3474335755110936\n",
      "4.373688964389013\n",
      "4.399887638804215\n",
      "4.426029317016701\n",
      "4.452113717899401\n",
      "4.478140560941211\n",
      "4.504109566249998\n",
      "4.5300204545556175\n",
      "4.555872947212913\n",
      "4.581666766204715\n",
      "4.607401634144827\n",
      "4.633077274281011\n",
      "4.658693410497968\n",
      "4.684249767320296\n",
      "4.7097460699154645\n",
      "4.735182044096764\n",
      "4.760557416326254\n",
      "4.785871913717707\n",
      "4.811125264039544\n",
      "4.836317195717756\n",
      "4.861447437838833\n",
      "4.886515720152671\n",
      "4.911521773075481\n",
      "4.936465327692689\n",
      "4.961346115761824\n",
      "4.986163869715407\n",
      "5.010918322663825\n",
      "5.0356092083982045\n",
      "5.060236261393271\n",
      "5.084799216810207\n",
      "5.109297810499499\n",
      "5.133731779003777\n",
      "5.15810085956065\n",
      "5.182404790105531\n",
      "5.206643309274453\n",
      "5.230816156406883\n",
      "5.254923071548524\n",
      "5.27896379545411\n",
      "5.302938069590193\n",
      "5.326845636137927\n",
      "5.350686237995835\n",
      "5.374459618782579\n",
      "5.398165522839713\n",
      "5.421803695234439\n",
      "5.445373881762337\n",
      "5.468875828950111\n",
      "5.492309284058307\n",
      "5.515673995084034\n",
      "5.538969710763674\n",
      "5.562196180575583\n",
      "5.585353154742785\n",
      "5.60844038423566\n",
      "5.631457620774619\n",
      "5.654404616832779\n",
      "5.6772811256386175\n",
      "5.700086901178634\n",
      "5.722821698199989\n",
      "5.7454852722131475\n",
      "5.768077379494503\n",
      "5.790597777089003\n",
      "5.813046222812757\n",
      "5.835422475255645\n",
      "5.857726293783911\n",
      "5.879957438542753\n",
      "5.902115670458901\n",
      "5.924200751243188\n",
      "5.946212443393111\n",
      "5.96815051019539\n",
      "5.990014715728507\n",
      "6.0118048248652505\n",
      "6.033520603275238\n",
      "6.055161817427437\n",
      "6.07672823459268\n",
      "6.098219622846162\n",
      "6.119635751069939\n",
      "6.140976388955413\n",
      "6.162241307005805\n",
      "6.183430276538626\n",
      "6.204543069688138\n",
      "6.2255794594077996\n",
      "6.246539219472711\n",
      "6.267422124482048\n",
      "6.288227949861481\n",
      "6.308956471865596\n",
      "6.329607467580296\n",
      "6.350180714925201\n",
      "6.370675992656034\n",
      "6.391093080367004\n",
      "6.411431758493173\n",
      "6.431691808312816\n",
      "6.451873011949778\n",
      "6.471975152375813\n",
      "6.4919980134129185\n",
      "6.511941379735662\n",
      "6.531805036873495\n",
      "6.551588771213059\n",
      "6.571292370000486\n",
      "6.590915621343682\n",
      "6.6104583142146085\n",
      "6.629920238451551\n",
      "6.64930118476138\n",
      "6.668600944721799\n",
      "6.68781931078359\n",
      "6.706956076272842\n",
      "6.726011035393175\n",
      "6.744983983227955\n",
      "6.7638747157424906\n",
      "6.782683029786238\n",
      "6.801408723094977\n",
      "6.820051594292989\n",
      "6.838611442895224\n",
      "6.857088069309453\n",
      "6.87548127483842\n",
      "6.893790861681973\n",
      "6.912016632939194\n",
      "6.930158392610516\n",
      "6.948215945599832\n",
      "6.96618909771659\n",
      "6.984077655677885\n",
      "7.001881427110536\n",
      "7.019600220553153\n",
      "7.037233845458197\n",
      "7.054782112194033\n",
      "7.072244832046962\n",
      "7.089621817223258\n",
      "7.106912880851182\n",
      "7.124117836982992\n",
      "7.141236500596948\n",
      "7.158268687599295\n",
      "7.175214214826248\n",
      "7.1920729000459565\n",
      "7.208844561960469\n",
      "7.2255290202076825\n",
      "7.242126095363276\n",
      "7.258635608942649\n",
      "7.275057383402833\n",
      "7.291391242144406\n",
      "7.307637009513389\n",
      "7.323794510803136\n",
      "7.339863572256214\n",
      "7.355844021066268\n",
      "7.371735685379882\n",
      "7.387538394298428\n",
      "7.403251977879901\n",
      "7.418876267140748\n",
      "7.434411094057687\n",
      "7.44985629156951\n",
      "7.465211693578884\n",
      "7.480477134954133\n",
      "7.495652451531017\n",
      "7.510737480114495\n",
      "7.525732058480482\n",
      "7.540636025377594\n",
      "7.555449220528879\n",
      "7.570171484633542\n",
      "7.584802659368662\n",
      "7.599342587390887\n",
      "7.6137911123381325\n",
      "7.628148078831261\n",
      "7.642413332475751\n",
      "7.656586719863362\n",
      "7.670668088573778\n",
      "7.684657287176252\n",
      "7.698554165231232\n",
      "7.712358573291979\n",
      "7.726070362906175\n",
      "7.739689386617519\n",
      "7.75321549796731\n",
      "7.766648551496028\n",
      "7.779988402744894\n",
      "7.793234908257423\n",
      "7.806387925580969\n",
      "7.819447313268257\n",
      "7.832412930878901\n",
      "7.845284638980918\n",
      "7.858062299152227\n",
      "7.870745773982134\n",
      "7.883334927072813\n",
      "7.895829623040773\n",
      "7.908229727518312\n",
      "7.920535107154963\n",
      "7.932745629618929\n",
      "7.944861163598504\n",
      "7.956881578803486\n",
      "7.96880674596658\n",
      "7.980636536844784\n",
      "7.992370824220773\n",
      "8.004009481904262\n",
      "8.015552384733368\n",
      "8.026999408575954\n",
      "8.038350430330961\n",
      "8.049605327929738\n",
      "8.060763980337347\n",
      "8.071826267553872\n",
      "8.082792070615707\n",
      "8.093661271596831\n",
      "8.104433753610083\n",
      "8.115109400808413\n",
      "8.125688098386133\n",
      "8.136169732580148\n",
      "8.146554190671182\n",
      "8.156841360984988\n",
      "8.167031132893547\n",
      "8.177123396816263\n",
      "8.187118044221142\n",
      "8.19701496762595\n",
      "8.20681406059938\n",
      "8.216515217762186\n",
      "8.226118334788328\n",
      "8.235623308406081\n",
      "8.245030036399159\n",
      "8.254338417607801\n",
      "8.26354835192987\n",
      "8.272659740321924\n",
      "8.281672484800279\n",
      "8.290586488442067\n",
      "8.299401655386278\n",
      "8.30811789083479\n",
      "8.316735101053387\n",
      "8.32525319337277\n",
      "8.333672076189549\n",
      "8.341991658967233\n",
      "8.350211852237202\n",
      "8.358332567599666\n",
      "8.366353717724621\n",
      "8.374275216352785\n",
      "8.382096978296525\n",
      "8.389818919440776\n",
      "8.397440956743942\n",
      "8.404963008238793\n",
      "8.412384993033342\n",
      "8.419706831311718\n",
      "8.426928444335024\n",
      "8.434049754442183\n",
      "8.441070685050775\n",
      "8.447991160657855\n",
      "8.454811106840774\n",
      "8.461530450257971\n",
      "8.468149118649766\n",
      "8.474667040839135\n",
      "8.48108414673248\n",
      "8.487400367320376\n",
      "8.493615634678317\n",
      "8.499729881967449\n",
      "8.50574304343528\n",
      "8.511655054416398\n",
      "8.517465851333158\n",
      "8.523175371696372\n",
      "8.528783554105976\n",
      "8.534290338251692\n",
      "8.539695664913676\n",
      "8.54499947596316\n",
      "8.550201714363066\n",
      "8.555302324168634\n",
      "8.56030125052801\n",
      "8.565198439682842\n",
      "8.56999383896886\n",
      "8.574687396816442\n",
      "8.579279062751162\n",
      "8.58376878739434\n",
      "8.588156522463569\n",
      "8.592442220773238\n",
      "8.596625836235036\n",
      "8.60070732385845\n",
      "8.604686639751243\n",
      "8.608563741119939\n",
      "8.612338586270267\n",
      "8.616011134607621\n",
      "8.619581346637494\n",
      "8.623049183965897\n",
      "8.62641460929978\n",
      "8.62967758644743\n",
      "8.632838080318859\n",
      "8.635896056926178\n",
      "8.638851483383972\n",
      "8.641704327909647\n",
      "8.64445455982377\n",
      "8.647102149550404\n",
      "8.649647068617426\n",
      "8.652089289656828\n",
      "8.654428786405015\n",
      "8.656665533703087\n",
      "8.658799507497111\n",
      "8.660830684838377\n",
      "8.662759043883646\n",
      "8.664584563895385\n",
      "8.666307225241988\n",
      "8.667927009397992\n",
      "8.669443898944271\n",
      "8.670857877568226\n",
      "8.672168930063961\n",
      "8.673377042332444\n",
      "8.674482201381661\n",
      "8.675484395326754\n",
      "8.67638361339015\n",
      "8.677179845901678\n",
      "8.67787308429867\n",
      "8.678463321126053\n",
      "8.678950550036433\n",
      "8.67933476579016\n",
      "8.679615964255385\n",
      "8.679794142408108\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n",
      "8.679869298332203\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAD8CAYAAABw1c+bAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvnQurowAAIABJREFUeJzt3XlcVXX+x/HXhx0RWQRlU8QVRRQVcKu0RU2zbM+mfXOcaZmmX03L/KYaf1NjM01T2uqUacvYYplOmZmVleWGioKCK6goCqIgssP9/v7g6qiBrHq4936ej8d9eO+533PO+3Dlw7ln+X7FGINSSinX4WZ1AKWUUueWFn6llHIxWviVUsrFaOFXSikXo4VfKaVcjBZ+pZRyMQ0WfhHpIiLfiUiGiGwWkd/ZpweLyNcist3+b1A9818qIltFZIeIPNbaG6CUUqpppKHr+EUkHAg3xqwXEX9gHXAlcDtw2Bgz3V7Qg4wxj542rzuwDRgD5ABrgRuNMVtafUuUUko1SoN7/MaYXGPMevvzYiADiAQmAXPtzeZS+8fgdMnADmPMLmNMJfCBfT6llFIW8WhKYxHpBgwCVgOdjTG5UPvHQUQ61TFLJLD3pNc5wNCG1hMSEmK6devWlGhKKeXS1q1bd8gYE9qYto0u/CLSHvgEeNAYc1REGjVbHdPqPLYkIlOAKQBdu3YlJSWlsdGUUsrlicjuxrZt1FU9IuJJbdF/3xjzqX3yQfvx/+PnAfLqmDUH6HLS6yhgf13rMMbMMsYkGmMSQ0Mb9UdLKaVUMzTmqh4B3gIyjDEvnPTWIuA2+/PbgIV1zL4W6CUiMSLiBUy2z6eUUsoijdnjHwncAlwkIqn2xwRgOjBGRLZTe9XOdAARiRCRxQDGmGrgPuArak8Kf2SM2XwWtkMppVQjNXiM3xizgrqP1QNcXEf7/cCEk14vBhY3N6BSSqnWpXfuKqWUi9HCr5RSLkYLv1JKuZgm3cCllLMqPVZEwYE9lB0toKL4MJUlR6guKcRUloCtGmOrBltN7cPNHfH0QTx8EA9v3Lz98PIPwTewE36BnQjo2Bk//0CrN0mpemnhVy7BVlND3r5d5GelUbI/EynYju+xvfhX5hFsO0QAJbRrxfUVG1/y3Ttz1CecCr9ITFA3/KL6E9ZzECFhXRE3/bKtrKOFXzkdW00Ne3ekkb91JdU5Gwg4kk505Q7CpIIwe5ujtCPPPZxCn0jy2g3B5h+OR0AkXh064u0XjE+HYHz9g/DxC8DT0xN3D088PLxwc3OjurqKivJSqirKqawopbykmLLCPMqK8qgqPkRNSQFuR/fhXbKPgPJcQktSaZ9fVttd4bdQhB/7PbtRFBSHR9ckIuIuIDy6t/4xUOeMFn7l8Gw1NWRnpJCXtgzvnJ+JKUklmmNEA2XGi91ePUnrdDl06kv7yH507t6fjp2i6NDMQuvp5Y2nl3ej2xubjcOHcsndnsqxvZsgP5MOR7cx8OBn+OZ9BClwmA7sbhdPZdfzCRs0nq69BugfAnXWNNgtsxUSExON9tWjzqS46DDbf15ITeYSehT9TDBHAdgvnckJGALRwwntM5wuvQbi4ellcdq6VVVWsDsjhYKtP+G2L4XIoxuIMLU9nxykI3sCk/HoO54+I6+kXfsAi9Oqtk5E1hljEhvVVgu/chRFh/PZ+t17+G5bRJ/yjXhJDUX4sd1/GKbHRUQmjCGiWx+rY7bIvl0Z5KxbjOfu7+lxLIUASig3nmT4JVHVawJ9Rk0mIFj7slK/pIVfOY3y0mNs/u4D3DZ/QlzJarykhhwJJ6fzRfgPmEifpEva7B59S1VXVZK5egklGxfSLf87OlNApfEgvf0I3BJupN8FV+Pl7WN1TNVGaOFXDm93xjpyv32NfvmL6UAJeQSzq/M4Og77FT0Hnudyx7+Nzcb21B85vOo9euctIZijHKEDWztdSsQl99K1d4LVEZXFtPArh1RdVUnq0rm0S51Dv6p0Ko07aR1G4Z18O32HX4a7h16LALXnBrasWEDN+n/Tv3gFXlJDmvdgqofcxYCLJuvPyUVp4VcOpaS4kLT/vEz0tjmEk0+OhJETcz29xv2ajp2jrI7Xph06sJftX75Mj90f0YnD5BLKnti7GHjF/fi0a291PHUOaeFXDqGo4CBbFkwnLudDOlBChmccFcn3MeCiG3Bzd7c6nkOprqok7dt5+Ka8TmzVFgoIYFvMLcRNeogOgR2tjqfOAS38qk0rLjpM+ifT6b/7HfyljA1+5+F74UPEJv6il2/VRMZmI2P1V1R//zwDylM4Sju2dLuDAdc+qpeEOjkt/KpNKi8rIfXj6cTumk0gx9jQbiQBE56ie/+hVkdzSttTf6Rk6TMklK7kEIHs7Hcvg6/8XZNuPlOOQwu/alOMzcaGpe8QtvpZIsxBNvkk4TvuSXoNusDqaC4hc/VSzLKn6Vu1mRwJ59DIpxh40Q0ud2WUs2vVwi8is4GJQJ4xpr992ofA8TtlAoFCY8wvricTkWygGKgBqhsbSgu/89iZtory/zxMXGUa2W5dKR79F+IvmGR1LJdjbDY2LZ9PwIppdLPtZaNvMsHXvECXnvFWR1OtpLUL/wXAMeCd44X/tPf/ARQZY6bV8V42kGiMOdSYMMdp4Xd8ZSXFbHz3URJz51Esfmzr9wBDrnrQaW+2chRVlRWs+/g5+m97FS+qWBd5E4NuflavAHICTSn8DX7XM8b8AByuZ0UCXA/Ma1JC5dTSfljAkeeHMOzA+6wPnoDbAxsYev0ftOi3AZ5e3gy76UnKf7OGjYEXM3z/XPL/nkTm6qVWR1PnUEsP8p0PHDTGbK/nfQMsFZF1IjKlhetSbVxx0WHWvHgj8d/eTg3ubB47j+Tfva99y7RBIWFdSfr9R6Rd9A7uVNN78fWseuVuSo8VWR1NnQMtLfw3cua9/ZHGmMHAeOBe+2GjOonIFBFJEZGU/Pz8FsZS51rG6q8ofnEoQ458ycrI2wn9QwpxIyZYHUs1IP6CSQQ8tJa1na5hWP7HHPlHEtvWL7c6ljrLml34RcQDuBr4sL42xpj99n/zgAVA8hnazjLGJBpjEkNDdQ/RUVRVVrDyXw/Se/ENgLD9so8Zfs9L+Pj6WR1NNZKffyBD732LLZd+iLuxEbPwala+8ydsNTVWR1NnSUv2+C8BMo0xOXW9KSJ+IuJ//DkwFkhvwfpUG5O3L4udfx/N8H1vsy5oPB1+v5rY5DFWx1LN1G/Ypfg+sJI0//MYvmsGm/92MYf277Y6ljoLGiz8IjIPWAn0EZEcEbnL/tZkTjvMIyIRIrLY/rIzsEJENgJrgC+MMUtaL7qyUvqKRbj/axRdK3eSkvQ8yQ/Oo32HIKtjqRYKCA5l0EOfsSb+aXqWb8bMGkXm2mVWx1KtTG/gUk1ibDZWvfcUyTtnkuMeCde/S3TsYKtjqbMga/NqPOffSidbPhv6P0HyNQ/pTV9tWKtezqnUcRXlpax78XqG75pBqv8oOj64Qou+E4uJG4r//SvI9B3M0M3/x9qZt1BZUW51LNUKtPCrRjmSn8uuf1xC4tGvWRk9lcEPLdBDOy4gIDiUuIeXsDLydpKPfM62F8ZxtLDA6liqhbTwqwbt2ZZK6auj6F65jXXJLzD8juf0K78LcffwYPg9L7E24Rn6lKdRMONCDuzdYXUs1QL626vOaMfGFfj/+3J8TRlZl3/IkAl3NTyTckpJV95H5sVvE1KTh9tbY9iVvtrqSKqZtPCrem1Z+SVhn15LBd6U3PS59peviL9gEoeuXwhAx/lXsW399xYnUs2hhV/VaeO3H9F9yS0UuHdE7v6KLr0GWh1JtRExcUOpvn0JJdKeiIU3kLH6K6sjqSbSwq9+YeO3H9H3+6nkeHTFf+pSOkf1sDqSamMiuvXB4+6vOOweTPTiW0j/caHVkVQTaOFXp0j7/lNiv/8tezy6EXrfUoI7RVodSbVRnSJjaDflKw66h9Nj2d1sWaX3ZzoKLfzqhPQVi+j17RRyPKII/e2XBASFWB1JtXEhYV0ImLqYPPdOdP3ydj3m7yC08CsAtq3/nu5f380B93CCfv0FAR07Wx1JOYjgTpH43vU5R9060GnRr8jastbqSKoBWvgVOTvSCVl0M4VugbSf8oUe3lFN1ikyBm5dRCVe+H90Lbm7t1odSZ2BFn4XV3AwB96/BsFQ86uPCQnranUk5aAiYmIpu2E+XlRSMfdaio40acRVdQ5p4XdhZSXFHP7XlXS0HebgxLl6yaZqsei+Q9hzyRtE1Oxj7+vXaN8+bZQWfhdlbDY2v34bPap2kDnyn3pzlmo1/c+7go2DptG/IpXU1+7A2GxWR1Kn0cLvola/9xSJxd+wuvtvGTT2ZqvjKCeTdOV9rIq6i+TCxaz5+G9Wx1Gn0cLvgjZ++xHJO2eyzv9Cht3yF6vjKCeVfMffSfUdxuAtfyNz9VKr46iTaOF3Mbm7txLzw4NkecTQb+q72sumOmvc3N2JmfI+B91CCfnyHh3GsQ1pzNCLs0UkT0TST5r2tIjsE5FU+2NCPfNeKiJbRWSHiDzWmsFV01VVVnD03VsRY8Pnpn/j6+dvdSTl5AKCQqi69h3amTLy5txETXW11ZEUjdvjnwNcWsf0fxpjEuyPxae/KSLuwCvAeKAfcKOI9GtJWNUyKW8/TJ/qTLYNfYbI7n2tjqNcREzcUDYPeop+lWmsee9/rY6jaEThN8b8ABxuxrKTgR3GmF3GmErgA2BSM5ajWsGm5Z8wPPcdVnecpH3qq3Mu8YrfkOJ/MUlZb7A15Vur47i8lhzgvU9ENtkPBdU1Bl8ksPek1zn2aXUSkSkikiIiKfn5+S2IpU5XdDifsOUPk+3WlYF3vWp1HOWCxM2N3nf9i3zpSPsvplJc1Jx9SdVamlv4XwN6AAlALvCPOtpIHdNMfQs0xswyxiQaYxJDQ0ObGUvVZdvcewk2hVRd8So+7dpbHUe5qA6BHSka/yphtjy2vPN7q+O4tGYVfmPMQWNMjTHGBvyL2sM6p8sBupz0OgrY35z1qeZL/frfJBV9RUqXO+iVcL7VcZSLix06lrVhkxla8Bmbf/rC6jguq1mFX0TCT3p5FZBeR7O1QC8RiRERL2AysKg561PNU3TkEFE/Pc4ut24MvuVZq+MoBcDAW//OPulMwLL/oayk2Oo4Lqkxl3POA1YCfUQkR0TuAv4mImkisgm4EPi9vW2EiCwGMMZUA/cBXwEZwEfGmM1naTtUHTLff4QgU4Rt0it4eftYHUcpAHz9/DlyyT+IMrlsfPdRq+O4JDGm3sPulklMTDQpKSlWx3Bo21N/pPuCy0npdA1D733L6jhK/cKal37FoMNL2D/5a6L7DrE6jsMTkXXGmMTGtNXbNp2QraYG8/lDHJEA+t6k/aSotqnnjX+nTHw4+tn/aEdu55gWfieU8tlMeldvI3vwY3QI7Gh1HKXqFNwpki197iO+YgMbvn7f6jguRQu/kyk9VkRM2otkevRlyMRfWx1HqTNKvPZhstyiCVs1jfKyEqvjuAwt/E5m48fPEsoRGDNNO2BTbZ6HpxclF/4fESaP1AUvWB3HZWhlcCIFB3OIz57LhnYjiR061uo4SjVK//MnkeY9iD7bZnHs6BGr47gELfxOZPv8p/GhguBJes2+cize454miKOkzf+r1VFcghZ+J3HowB4S8j5jfdClRPdJsDqOUk3Se/BoNvidR/zudyg8dMDqOE5PC7+T2PHZdDypJmLiH62OolSzBE38M+2ljIyFz1sdxelp4XcCR/JzGZA7nw0BFxPVs7/VcZRqlm59E9nQbgR9986jpLjQ6jhOTQu/E8hc+Dd8qCR0gu7tK8fme9HDBHKMtP/MtDqKU9PC7+DKS48Rm/MxG/2GEx072Oo4SrVIbOLFbPaKJ2bb21RWlFsdx2lp4XdwaUveIohiPEf+1uooSrWK6mEP0JkC0pa9Z3UUp6WF34EZm42O6bPZ5daNuOGXWR1HqVYRP+oa9klnfDfOsTqK09LC78C2rFpCd1s2h+Lu0Lt0ldNwc3dnb48b6VeZRtaWtVbHcUpaLRxY2arZHKUdA8bfbXUUpVpV7KW/ocJ4kvetjhF9Nmjhd1BHCwuIK/qejI5jdRxd5XQCQ8LYFHgRcflfUl56zOo4TkcLv4PKXDYXX6kkcPhtVkdR6qzwTbqZ9lLG5u8+sDqK02nM0IuzRSRPRNJPmvZ3EckUkU0iskBEAuuZN9s+RGOqiOiQWq2oQ+ZH7HbrQu/Bo62OotRZ0XfYBPIIxj39Y6ujOJ3G7PHPAS49bdrXQH9jzABgG/D4Gea/0BiT0NghwVTD9mdvJbY6g/3Rk/SkrnJa7h4e7AyfQFzpWg7n7bM6jlNpsGoYY34ADp82bal9MHWAVUDUWcim6rFnxTwAup5/s8VJlDq7ws6/HU+pYft3ek1/a2qN3cU7gS/rec8AS0VknYhMOdNCRGSKiKSISEp+fn4rxHJeQdlfssO9B5Hd+1odRamzKqZfEnvcImm3a4nVUZxKiwq/iPwRqAbqGzBzpDFmMDAeuFdELqhvWcaYWcaYRGNMYmhoaEtiObWDOTvpU53JoS6nH31Tyjnt63whseUbKTpyyOooTqPZhV9EbgMmAjcZY0xdbYwx++3/5gELgOTmrk/Vyv6p9kRXxIjrLU6i1LkRNPiq2sM9P31qdRSn0azCLyKXAo8CVxhjSutp4yci/sefA2OB9Lraqsbzzv6OHAmja28dbEW5ht6DL+QQgUjmF1ZHcRqNuZxzHrAS6CMiOSJyF/Ay4A98bb9U83V72wgRWWyftTOwQkQ2AmuAL4wxeqCuBSoryulduoF9wcOsjqLUOePm7k5W4HB6HEvBVlNjdRyn4NFQA2PMjXVMfquetvuBCfbnu4CBLUqnTrEt5Wv6SwVefcZYHUWpc0q6jyJw/ZfsSF9Fz4EjrY7j8PQicAdSvHkpVcadnkMnWB1FqXMqOnE8AIfSllqcxDlo4Xcggfkp7PTsjX9AsNVRlDqnQiO6sdstinY5P1kdxSlo4XcQFeWldK/cTmGIjrKlXNOB4GR6lKVRU13dcGN1Rlr4HURW2s94SxVeMcOtjqKUJdy6JOEn5ezZtsHqKA5PC7+DKNy6AoCuA0dZnEQpa3TuOwKAQ5k/W5zE8WnhdxCeBzawXzoREtbV6ihKWSKqRzxH8cO2b53VURyeFn4HEVK6g4PtelsdQynLuLm7s9u7Dx0L9T7QltLC7wDKS48RVbOP8mDtlE25tpKgvnSp3qMneFtIC78D2LttA+5i8ImKtzqKUpZy69wXb6lif3aG1VEcWoN37irrHcmqvYohpIdjXMpZVVVFTk4O5eXlVkdRjeTj40NUVBSenp5WRzmjwOh42AiHdm2kS0/dEWouLfwOoCZ/B1XGnYhujnGoJycnB39/f7p164aIWB1HNcAYQ0FBATk5OcTExFgd54wietb2AlOeu8XiJI5ND/U4AK/iPRx064S7h2P8nS4vL6djx45a9B2EiNCxY0eH+IbWvkMQeQTjcWSX1VEcmhZ+B+Bfto/D3hFWx2gSLfqOxZE+r8OeYfiW5Vodw6Fp4XcAodW5lPl1sTqGQ2nfvr3VERo0Z84cRIRvvvnmxLQFCxYgIsyfP7/Ry1m+fDkTJ05scRtHUeITRmDlQatjODQt/G1c6bEigijG1kHHs7dSdStcPljXMuLj45k3b96J1x988AEDB2pv5mdS2T6CUNsh7Zu/BbTwt3GF+bVfad07hFmcxPHl5+dzzTXXkJSURFJSEj/9VNvT45o1axgxYgSDBg1ixIgRbN26FajdI7/uuuu4/PLLGTt2LMuXL2f06NFce+21xMbGctNNN3F81NF169YxatQohgwZwrhx48jNrf3cRo8ezRNPPMGoUaN46aWXfpHp/PPPZ82aNVRVVXHs2DF27NhBQsJ/R1f75ptvGDRoEPHx8dx5551UVFQAsGTJEmJjYznvvPP49NP/DklYUlLCnXfeSVJSEoMGDWLhwoVn54dpIbfALnhLFYfz91kdxWE1eLZQRGZTO7ZunjGmv31aMPAh0A3IBq43xhypY95LgZcAd+BNY8z0VkvuIooL9gPgHeiYhf/P/9nMlv1HW3WZ/SI68NTlcU2e73e/+x2///3vOe+889izZw/jxo0jIyOD2NhYfvjhBzw8PFi2bBlPPPEEn3zyCQArV65k06ZNBAcHs3z5cjZs2MDmzZuJiIhg5MiR/PTTTwwdOpT777+fhQsXEhoayocffsgf//hHZs+eDUBhYSHff/99nZlEhEsuuYSvvvqKoqIirrjiCrKysoDak+S3334733zzDb179+bWW2/ltddeY+rUqdxzzz18++239OzZkxtuuOHE8p555hkuuugiZs+eTWFhIcnJyVxyySVN/lm1ZR7+nQEoPnxQuzBppsZcJjKH2qEW3zlp2mPAN8aY6SLymP31oyfPJCLuwCvAGCAHWCsii4wxeh1WE5QdOQBAuyDHLPxtybJly9iy5b///Y4ePUpxcTFFRUXcdtttbN++HRGhqqrqRJsxY8YQHPzf8Q+Sk5OJiqo97JaQkEB2djaBgYGkp6czZkztyGg1NTWEh4efmOfkwlyXyZMnM2PGDIqKivjHP/7Bs88+C8DWrVuJiYmhd+/arjpuu+02XnnlFUaPHk1MTAy9evUC4Oabb2bWrFkALF26lEWLFvH8888DtX889uzZ07wfWBvl3aEjAKWF+RYncVyNGXrxBxHpdtrkScBo+/O5wHJOK/xAMrDDPgQjIvKBfT4t/E1QebT2JJZ/sGMW/ubsmZ8tNpuNlStX4uvre8r0+++/nwsvvJAFCxaQnZ3N6NGjT7zn5+d3Sltvb+8Tz93d3amursYYQ1xcHCtXrqxzvacv43TJycmkp6fj6+t7osgDJw4j1aW+q3CMMXzyySf06dPnlOkHDzrPyVDfDiEAVBQXWJzEcTX3GH9nY0wugP3fTnW0iQT2nvQ6xz5NNYGtvPYwiV9AR4uTOL6xY8fy8ssvn3idmpoKQFFREZGRtf8158yZ0+Tl9unTh/z8/BOFv6qqis2bNzdpGX/9619P7OkfFxsbS3Z2Njt27ADg3XffZdSoUcTGxpKVlcXOnTsBTjk5PG7cOGbOnHnij8aGDc7Xd71fYCgA1ccOWZzEcZ3Nk7t17ZLUuwsjIlNEJEVEUvLz9SvccaayFAAf3zPvNapTlZaWEhUVdeLxwgsvMGPGDFJSUhgwYAD9+vXj9ddfB+APf/gDjz/+OCNHjqSmGVeKeHl5MX/+fB599FEGDhxIQkICP//ctD7jx48fz4UXXnjKNB8fH95++22uu+464uPjcXNzY+rUqfj4+DBr1iwuu+wyzjvvPKKjo0/M86c//YmqqioGDBhA//79+dOf/tTk7Wnrju8E2cqKLE7iuORMXydPNKo91PP5SSd3twKjjTG5IhIOLDfG9DltnuHA08aYcfbXjwMYY/7a0PoSExNNSkpKEzfFOa2c9QBD9r2H158PWx2l0TIyMujb1zG6l1D/5SifW0V5Kd7Tw1nV7V6G3f5swzO4CBFZZ4xJbEzb5u7xLwJusz+/DajrmrG1QC8RiRERL2CyfT7VBFJVSrl4N9xQKRfh5eUDgKmpsDiJ42qw8IvIPGAl0EdEckTkLmA6MEZEtlN71c50e9sIEVkMYIypBu4DvgIygI+MMU078KmQmgoq8bI6hlJthri5UWncoabS6igOqzFX9dxYz1sX19F2PzDhpNeLgcXNTqfAgfpQUepcqcIT0cLfbHrnbpsnuGGzOoRSbYpgqPv6EdUYWvjbOnGz/ydXSh3nQTXGvW0PGtOWaeFv83SPX6mTGZsNL6lB3LTwN5cW/jbOuHvhZaoabqhO8cwzzxAXF8eAAQNISEhg9erVZ2w/evRoGrqE+LPPPjuly4cnn3ySZcuWtTjr8uXLERHeeuutE9M2bNiAiJzoeqExsrOz6d+/f4vbtHU1NbW9nOoef/Np4W/jjHcHfKWS6io9kdVYK1eu5PPPP2f9+vVs2rSJZcuW0aVLy8czOL3wT5s2rdU6QIuPj+fDDz888Vq7Z65fRXntTY3irle7NZcW/jZOvGsHFCk51ro9XDqz3NxcQkJCTvSrExISQkRE7Qhm9XVzfLKTB3GZP38+t99+Oz///DOLFi3ikUceISEhgZ07d3L77befGDClvuV269aNp556isGDBxMfH09mZmadmbt27Up5eTkHDx7EGMOSJUsYP378ifdTU1MZNmwYAwYM4KqrruLIkdrOcNetW8fAgQMZPnw4r7zyyon2NTU1PPLIIyQlJTFgwADeeOONlvxI25TiwtquGtzaBVmcxHE5xiCuLszNxx+AsuIjBASFWJymGb58DA6kte4yw+JhfP09fI8dO5Zp06bRu3dvLrnkEm644QZGjRpVbzfHDz74YIOrHDFiBFdccQUTJ07k2muvPeW9hpYbEhLC+vXrefXVV3n++ed5880361zHtddey8cff8ygQYMYPHjwKR3C3XrrrcycOZNRo0bx5JNP8uc//5kXX3yRO+6448T0Rx555ET7t956i4CAANauXUtFRQUjR45k7NixDjXEYn1Ki2o7Z/Pw08LfXLrH38a5+wYCUHrUcbpssFr79u1Zt24ds2bNIjQ0lBtuuIE5c+bU2c3xDz/80OL1NbTcq6++GoAhQ4aQnZ1d73Kuv/56Pv74Y+bNm8eNN/739pmioiIKCwsZNWrUKcs/ffott9xyYp6lS5fyzjvvkJCQwNChQykoKGD79u0t3ta2oLy49nfBq31wAy1VfXSPv43ztffDX1LgoKMNnWHP/Gxyd3dn9OjRjB49mvj4eObOnXvKyFZncvJecXl5eYPtG+rv6vie+/FunOsTFhaGp6cnX3/9NS+99FKDHb0ZY87YPfPMmTMZN27cKdPP9IfHURzvjtmng/ZY21y6x9/G+YfWDvpRfmS/xUkcx9atW0/Zu01NTSU6Orrebo5P17lzZzIyMrDZbCxYsODEdH9/f4qLi3/RvrHLbYxp06bx3HPP4e7ufmJaQEAAQUFB/Pjjj6csPzAwkICAAFasWAHA+++/f2ImGMooAAAYb0lEQVSecePG8dprr50YVGbbtm2UlJQ0K1NbU1lYO6xlQKiOQ91cusffxgV3rr0apboo1+IkjuPYsWPcf//9FBYW4uHhQc+ePZk1a9Yp3RxXV1eTlJTE1KlTfzH/9OnTmThxIl26dKF///4cO3YMqB0p65577mHGjBknTuoCjV5uY4wYMaLO6XPnzmXq1KmUlpbSvXt33n77bQDefvtt7rzzTtq1a3fK3v3dd99NdnY2gwcPxhhDaGgon332WbMytTW2ohyqjDvBnbTwN1ejumU+17Rb5lMdeyqM9E4TGXZv3ScF2xpH6d5XncpRPre1/7yOLkUbCHt6h9VR2pRz0S2zOocOuYfiXeKgx/iVamXtyg5wxDPU6hgOTQu/Azji04Xg8r0NN1TKBQRVHaTEJ7zhhqpeWvgdQEWHboTX5FJzhitClHIF5aXHCLPlURXU0+ooDk0LvwNwC+mJl1RzMGen1VEarS2eO1L1c5TPa9+OTbiJwSusT8ONVb208DsAv4hYAA5ltfIdsGeJj48PBQUFDlNMXJ0xhoKCAnx8fKyO0qAje9IBCI527I7mrNbsyzlFpA/w4UmTugNPGmNePKnNaGrH482yT/rUGDOtuet0VVGxSbAUSvZsAK5tsL3VoqKiyMnJIT8/3+ooqpF8fHyIimr7l0dWH8ikxggRPeKtjuLQml34jTFbgQQAEXEH9gEL6mj6ozFmYnPXoyAgOJT90gmv/HSrozSKp6cnMTExVsdQTsi3IJ0c9yiifdpZHcWhtdahnouBncaY3a20PHWag+1606lkm9UxlLKMsdmIKsskz7+f1VEcXmsV/snAvHreGy4iG0XkSxGJa6X1uZzykP50MfspLtLO2pRrOpizk44UYQsfZHUUh9fiwi8iXsAVwMd1vL0eiDbGDARmAvXeMy4iU0QkRURS9NjwL/nFJAOQvfF7i5MoZY39W34CILDnUIuTOL7W2OMfD6w3xhw8/Q1jzFFjzDH788WAp4jU2am8MWaWMSbRGJMYGqp35Z2u++CLqDHCsW0t70ZYKUdUmbWKSuNBdJwW/pZqjcJ/I/Uc5hGRMLH3Gysiyfb1FbTCOl1O+w5B7PLoQYe8tVZHUcoSIYfWsN27Lz6+flZHcXgtKvwi0g4YA3x60rSpInK8a8JrgXQR2QjMACYbvbi72QpCEulZkXlizFGlXEVRwUG6V+/iaNhwq6M4hRYVfmNMqTGmozGm6KRprxtjXrc/f9kYE2eMGWiMGWaMOfPIEuqMvHucj7dUsWPdd1ZHUeqc2rXua9zEENDvYqujOAW9c9eB9Bw6gUrjztH0xVZHUeqcqtz2LWXGix4JF1gdxSlo4Xcg/gHBbPOJJ+zgj1ZHUeqcMTYbXQp+ZGu7wXjrjVutQgu/gznW5UJibLs5sMc5Bs5WqiHZGWuJMHlU9hjXcGPVKFr4HUx44hUA7F75aQMtlXIOB9bW9gTTfcQ1FidxHlr4HUzX3gnscYuk/c7PrY6i1DnRMecbtnn0JiQi2uooTkMLv4MRNzf2RY6nb0Uah/Zr10jKue3PyqR39TYKuoy1OopT0cLvgCJG/Ao3Mez84d9WR1HqrNr9/RwAuo2+1dogTkYLvwOK7juELLdoOuxcZHUUpc4aY7MRsedzMjzjCI/WEbdakxZ+B3UgeiJ9q7awd/tGq6ModVbsTFtJtG0vR3tdZXUUp6OF30H1GvNrqo0bOd++aXUUpc6KghWzqTQe9LnoFqujOB0t/A4qJCKaNL9h9MpdRFVlhdVxlGpVpceK6Ju/mE0BowkMCbM6jtPRwu/AZMhthFBI+ncfWB1FqVaV/tXbdKAUv5FTrI7ilLTwO7D+F1zNQTriuX621VGUalVBW94l260rsUljrI7ilLTwOzAPTy+yut9E/4pUdm7Sjk+Vc8hM+YZeNTs42OcmxE1L1NmgP1UH13fiA5Qabw5/86LVUZRqFWXfvUARfvSfMLXhxqpZtPA7uIDgUNI6Xc7AwmXk78+2Oo5SLbJnWyoDj/1ERtRk/PwDrY7jtLTwO4Go8Q/hjo2dC6dbHUWpFjnw5d+pxINelz9kdRSn1tKhF7NFJE1EUkUkpY73RURmiMgOEdkkIoNbsj5Vt8jucawPHMPAA59w6MBeq+Mo1SwHc3aScHgJG0Muo2PnKKvjOLXW2OO/0BiTYIxJrOO98UAv+2MK8ForrE/VIezyJ/Giih0LnrE6ilLNkv3p0wBET/pfa4O4gLN9qGcS8I6ptQoIFJHws7xOl9SlZzzrA8fa9/r3WB1HqSbJ2ZHOkILP2dDpSsK69rI6jtNraeE3wFIRWScidd1pEQmcfOwhxz5NnQXhlz+JJ9XsnP+U1VGUapIDi56iCg96XKP/d8+Flhb+kcaYwdQe0rlXRE4fCVnqmMfUtSARmSIiKSKSkp+f38JYrimqZ3/WhV7JkPzP2J253uo4SjXKzrRVDC76htSIyYSEdbU6jktoUeE3xuy3/5sHLACST2uSA3Q56XUUsL+eZc0yxiQaYxJDQ0NbEsul9br+L5ThzZGFj1sdRakGGZuN8v88TJG0p991T1odx2U0u/CLiJ+I+B9/DowF0k9rtgi41X51zzCgyBiT2+y0qkHBnSLZ3OMeEspWkfbDQqvjKHVGG76aS1xlGtviHiQgWHf4zpWW7PF3BlaIyEZgDfCFMWaJiEwVkeO33C0GdgE7gH8Bv21RWtUoCdc9xn7pRIflf6SyotzqOErVqbz0GOGrn2GnewyJVz1odRyX0uzCb4zZZYwZaH/EGWOesU9/3Rjzuv25Mcbca4zpYYyJN8b84lp/1fp8fP3IO+//iLbtZf28aVbHUapOqf9+knDyKb/4Wdw9PKyO41L0zl0nlXDxZNb7XUBC1iz27dpsdRylTpG1eTVD9s5hbcBY4kZMsDqOy9HC78SifjWDajwo+Oh+jM1mdRylAKiprqZywf0Uix+9bplpdRyXpIXfiXWKjGFz398xoHwdaxfMsDqOUgCs/eiv9Kneyq7EP+noWhbRwu/kkq77A5u9BhK36a/sz8q0Oo5ycbu3pjJw6ww2+g5lyIS7rY7jsrTwOzk3d3c63vwWNoTCf99FTXW11ZGUi6qsKKfqozspF28ib/mXDrJiIf3Ju4Cwrr3IHPQn+lWls/bff7Y6jnJR6+Y8Qs+anWSPmE5IRLTVcVyaFn4XkXjFb1jf/gISd75M5uqlVsdRLib9p/8wdP+7rA6+gkFjb7Y6jsvTwu8ixM2NnnfP4YBbJ4K//DWH8/ZZHUm5iLx9WYR/fS973SOJv/Nlq+MotPC7lA6BHSm/cjYBppic2bdiq6mxOpJycpUV5Rx++0Z8TAVc/y7t2gdYHUmhhd/l9Bw4ktT+jzOgPIXVbz9sdRzl5Db867fEVmeQOXQ60bE6AF9boYXfBSVf83vWBF3G8JzZpHw+y+o4ykmtWTCDoYc+YVXnGxky4Q6r46iTaOF3QeLmRsLU2Wzxiid+7RNsTfnW6kjKyaSvWMSg1KdJ8x7MkLtesjqOOo0Wfhfl5e1D+D0fc8gtmI6f38GBPdutjqScxO7M9XRdNpV97pFE/2Y+nl7eVkdSp9HC78KCQsOpvn4eXlRROWcSR/J1qATVMocO7MXzw8lU4on3bfPpENjR6kiqDlr4XVx03yHsG/82nWryyH/jCkqKC62OpBxU0eF8js6aSKCtkMNXzCU8uo/VkVQ9tPAr+g4dR+b5M+letYNdL19FRXmp1ZGUgykpLuTAqxOJqslh58Vv0HvwaKsjqTPQwq8ASLjkRtYnTCO+Yj0ZM67WkbtUo5WXlZD18iR6VG0jfcSLxF9wldWRVANaMuZuFxH5TkQyRGSziPyujjajRaRIRFLtDx1NuQ1Lvup+Vvd9goTSlWx56Urd81cNKispZttLl9O/IpUNg/7C4HG3WB1JNUJL9virgf8xxvQFhgH3iki/Otr9aIxJsD90HMA2bugNj54o/hkzrtbir+pVUlzIrpcuo3/ZetYM/D+SrrzX6kiqkVoy5m6uMWa9/XkxkAFEtlYwZZ2Ti//WFyfqCV/1C8VFh9kzYzx9KtJYn/gcyVc9YHUk1QStcoxfRLoBg4DVdbw9XEQ2isiXIhJ3hmVMEZEUEUnJz89vjViqBYbe8ChrB0wjrmw9+14ao5d6qhMOHdjDwRmX0LNyK5uGvUDi5b+2OpJqohYXfhFpD3wCPGiMOXra2+uBaGPMQGAm8Fl9yzHGzDLGJBpjEkNDQ1saS7WCpKt/x6aRL9O1Kovi1y4md/dWqyMpi+3emkrlGxcTUZ3DltFvMHi8dsXgiFpU+EXEk9qi/74x5tPT3zfGHDXGHLM/Xwx4ikhIS9apzq1BY29m1/j3CLQdwePtcWxb/73VkZRFMlcvJWDeZXibCvZdOZ+BF15ndSTVTC25qkeAt4AMY8wL9bQJs7dDRJLt6yto7jqVNfoNu5SC6xdRJZ50XXgNKV/8y+pI6hxb+9nLxCz+FcXSgfJbv6LXoAusjqRaoCV7/COBW4CLTrpcc4KITBWRqfY21wLpIrIRmAFMNsaYFmZWFojpl4TPb5aT5dWbxLUPs/LN32t//i6gqrKCVa/cTVLqH9nuE4f/vd8R2b2v1bFUC0lbrMOJiYkmJSXF6hiqDhXlpWx8/S6SCxez0TeZ6LveJTAkzOpY6iw4nLeP3DdvJK5yI6s6Tybx7pl4eHpZHUvVQ0TWGWMSG9NW79xVTeLt046kB95ndd/H6Vu6nvKXR5K5dpnVsVQr2/zTF1S/eh49K7awNuFZhv3mDS36TkQLv2oycXNj6A2PsfvKBdjEnR6fX8+q957WQz9OoLqqklVvPkTfpTdRIT7svXqh3pjlhLTwq2brNegC/B74mXS/YQzb8U8ynrtQL/l0YPt2ZbD9b6MZlvMW64IuJfihlfQcONLqWOos0MKvWiQgKISEhz9nTfzTdKvYiv/sUaxZMANjs1kdTTWSraaG1R/8laC5o+hSuYuUwc+R9OAH+PkHWh1NnSV6cle1mv1ZmRTOu5t+lWls9B1Kp8kztU/2Nm7frs0UfvBr4irT2OSTSKeb3iCsS0+rY6lm0JO7yhIRMbHEPvo9q3r9D71KUwmYfT6r3n2SqsoKq6Op01SUl7JyzmMEzx1N14odrB0wjfg/fK1F30XoHr86Kw7s2U7uBw8wqPRnsty6UTb2OfoNu9TqWArY9N18gn/4X6JMLuv9LiDyxhfpHNXD6liqhXSPX1kurGsvBv3hSzaMeAVf2zH6LbmBDX+/jL070qyO5rJ2b01lw9/GM+D7uzAIaRe+zeBH/qNF3wXpHr8668pKikn96C8MzH4bD6pZ3/ka+lw3jaDQcKujuYS8fVlkz/9fhhz+gjJ8SOt+F4Nv+CPePu2sjqZaUVP2+LXwq3Pm0IE97ProCYYUfE453myKvIHYqx7XPwBnScHBHLZ99hwJ+z/AnRrWd76G3tc+TXAnHTbDGWnhV21adkYKBYv/wqCjyymz/wHoc+WjWpBaycGcnWQtms7Ag5/hTRXrAy4m4qpniIiJtTqaOou08CuHsDtjHYcW/4VBR7+jEg82dbyUzmN+T3TfIVZHc0hZm1eTv2wGCYe/RIDUoLF0nvAYXXsnWB1NnQNa+JVD2b01lQNf/YOBBV/iI1Vs8knCDP01/c+/CncPD6vjtWnVVZWkfTsPr3VvEle5iXLjycaQy+hy+RNEdNN7KFyJFn7lkI7k55L5+Yv02v0BIRRygBCyulxJ9MVTtIidJu2HBfT8ZgrF0p5OHCaXUHZ3v5HYCfdqb6kuSgu/cmgV5aWkf/shnpveo3/ZOgC2+AyktPeV9Bn9KwI6drY4oTX2bEul/KN76F297cS0AgLYM+JZBlw0Wb8duTgt/Mpp5O7eSvY3b9Jl7yKizAGqjDtbfAdT0WcSPUde7fQnhHdu+hn57Dd0t2WfMr3Y+LJv4nvEJl1iTTDV5mjhV07H2GzsTPuZ/FUfEn1gCREmD5sRdnj2oiB8FMEDJ9Az4QKH3+stKykm9eNnGJ79Wp3vr4n/M0lXPYC46b2X6lTnrPCLyKXAS4A78KYxZvpp74v9/QlAKXC7MWZ9Q8vVwq/O5MQfgfX/IWjf9/SqysRdDEdpR5ZPHKXhyQTGjqL7wPPb/E1Khw7sZcfn/2Tg3nfxlcpfvF9pPEhLfo7B4+/UYq/O6JwUfhFxB7YBY4AcYC1wozFmy0ltJgD3U1v4hwIvGWOGNrRsLfyqKQoPHWDHqkXUZK2g85H1dLPtBaDSuLPXI5oC/1hsnePpEDOYiJ4JBAR3sqSIZmekkPvjO8TsX0wY+fW2Wxswji7XPENY117nMJ1ydE0p/C35XpwM7DDG7LKv9ANgErDlpDaTgHfsA6yvEpFAEQk3xuS2YL1KnSIwJIzEiVOAKUDt1UHZG76hPGs1fkc207NwBcGFi8E+RsxR/DjgEclR3y5UdeiKW4dwvALD8A2OpENIFH6BIfi179DooQZrqqspOVZE0aH95Hz3Jr33LaAjRb9o183+ON3q0GuJGv/wiUHMk5r8E1CqaVpS+COBvSe9zqF2r76hNpHALwq/iJz4ze3atWsLYilXFxQaTtDYm4GbgdpDQ/kH9rA/cw1luZnIkSzaFWcTcSydzke/xV3q/tZbbjwpFV8q8MaIAIKN2n89TBU+lONjKvCRKjoAHYAuZ8iVSyjZERMIP/9WuvX9745Zg1+BlWplLSn8Use003+DGtOmdqIxs4BZUHuopwW5lDqFuLkRGtGN0Ihuv3ivprqaQ4f2U5SXw7GCfVQU5mIrLcRUliAVxUhVCW7VZYBBjAEMGINx98Lm4Yvx8MV4+SFefrj7d8InMIx2wREEdAwnqFPkKSebw+0PpazWksKfw6k7OFHA/ma0Ucoy7h4ehIR1JSRMv2Uq19GSM1xrgV4iEiMiXsBkYNFpbRYBt0qtYUCRHt9XSilrNXuP3xhTLSL3AV9ReznnbGPMZhGZan//dWAxtVf07KD2cs47Wh5ZKaVUS7TobhdjzGJqi/vJ014/6bkB7m3JOpRSSrUuvSNEKaVcjBZ+pZRyMVr4lVLKxWjhV0opF6OFXymlXEyb7JZZRPKB3Wdh0SHAobOwXCs407aAc22PM20LONf2ONO2wKnbE22MCW3MTG2y8J8tIpLS2N7r2jpn2hZwru1xpm0B59oeZ9oWaP726KEepZRyMVr4lVLKxbha4Z9ldYBW5EzbAs61Pc60LeBc2+NM2wLN3B6XOsavlFLK9fb4lVLK5Tl94ReR60Rks4jYRCTxpOndRKRMRFLtj9fPtJy2or7tsb/3uIjsEJGtIjLOqozNISJPi8i+kz6PCVZnag4RudT+898hIo9ZnaclRCRbRNLsn4fDDYItIrNFJE9E0k+aFiwiX4vIdvu/QVZmbIp6tqdZvzdOX/iBdOBq4Ic63ttpjEmwP6ae41zNVef2iEg/asdEiAMuBV4VEfdzH69F/nnS57G44eZti/3n/QowHugH3Gj/XBzZhfbPwxEvgZxD7e/CyR4DvjHG9AK+sb92FHP45fZAM35vnL7wG2MyjDFbrc7RWs6wPZOAD4wxFcaYLGrHQEg+t+lcXjKwwxizyxhTCXxA7eeiLGCM+QE4fNrkScBc+/O5wJXnNFQL1LM9zeL0hb8BMSKyQUS+F5HzrQ7TQvUNbO9I7hORTfavtA7zFfwkzvAZnMwAS0VknYhMsTpMK+l8fBRA+7+dLM7TGpr8e+MUhV9ElolIeh2PM+1t5QJdjTGDgIeAf4tIh3OT+MyauT2NHtjeKg1s12tADyCB2s/mH5aGbZ42/xk00UhjzGBqD13dKyIXWB1I/UKzfm9aNAJXW2GMuaQZ81QAFfbn60RkJ9AbsPwkVnO2BwcY2L6x2yUi/wI+P8txzoY2/xk0hTFmv/3fPBFZQO2hrLrOlTmSgyISbozJFZFwIM/qQC1hjDl4/HlTfm+cYo+/OUQk9PjJTxHpDvQCdlmbqkUWAZNFxFtEYqjdnjUWZ2o0+y/hcVdRexLb0awFeolIjIh4UXuyfZHFmZpFRPxExP/4c2AsjvmZnG4RcJv9+W3AQguztFhzf2+cYo//TETkKmAmEAp8ISKpxphxwAXANBGpBmqAqcaYVjlxcjbVtz32ge4/ArYA1cC9xpgaK7M20d9EJIHaQyPZwK+tjdN0xphqEbkP+ApwB2YbYzZbHKu5OgMLRARq68S/jTFLrI3UNCIyDxgNhIhIDvAUMB34SETuAvYA11mXsGnq2Z7Rzfm90Tt3lVLKxbjsoR6llHJVWviVUsrFaOFXSikXo4VfKaVcjBZ+pZRyMVr4lVLKxWjhV0opF6OFXymlXMz/A0Rydw3wOBd/AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample_time = 0.01\n",
    "time_end = 20\n",
    "model.reset()\n",
    "solution_model.reset()\n",
    "\n",
    "t_data = np.arange(0,time_end,sample_time)\n",
    "x_data = np.zeros_like(t_data)\n",
    "y_data = np.zeros_like(t_data)\n",
    "x_solution = np.zeros_like(t_data)\n",
    "y_solution = np.zeros_like(t_data)\n",
    "\n",
    "for i in range(t_data.shape[0]):\n",
    "    x_data[i] = model.xc\n",
    "    y_data[i] = model.yc\n",
    "    \n",
    "    if model.delta < np.arctan(2/10):\n",
    "        model.step(np.pi, model.w_max)\n",
    "    else:\n",
    "        model.step(np.pi, 0)\n",
    "        \n",
    "    x_solution[i] = solution_model.xc\n",
    "    y_solution[i] = solution_model.yc\n",
    "    \n",
    "    if solution_model.delta < np.arctan(2/10):\n",
    "        solution_model.step(np.pi, model.w_max)\n",
    "    else:\n",
    "        solution_model.step(np.pi, 0)    \n",
    "    print(max(x_solution))\n",
    "plt.axis('equal')\n",
    "plt.plot(x_data, y_data,label='Learner Model')\n",
    "plt.plot(x_solution, y_solution,label='Solution Model')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are some other example trajectories: a square path, a spiral path, and a wave path. Uncomment each section to view."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample_time = 0.01\n",
    "time_end = 60\n",
    "model.reset()\n",
    "solution_model.reset()\n",
    "\n",
    "t_data = np.arange(0,time_end,sample_time)\n",
    "x_data = np.zeros_like(t_data)\n",
    "y_data = np.zeros_like(t_data)\n",
    "x_solution = np.zeros_like(t_data)\n",
    "y_solution = np.zeros_like(t_data)\n",
    "\n",
    "# maintain velocity at 4 m/s\n",
    "v_data = np.zeros_like(t_data)\n",
    "v_data[:] = 4 \n",
    "\n",
    "w_data = np.zeros_like(t_data)\n",
    "\n",
    "# ==================================\n",
    "#  Square Path: set w at corners only\n",
    "# ==================================\n",
    "w_data[670:670+100] = 0.753\n",
    "w_data[670+100:670+100*2] = -0.753\n",
    "w_data[2210:2210+100] = 0.753\n",
    "w_data[2210+100:2210+100*2] = -0.753\n",
    "w_data[3670:3670+100] = 0.753\n",
    "w_data[3670+100:3670+100*2] = -0.753\n",
    "w_data[5220:5220+100] = 0.753\n",
    "w_data[5220+100:5220+100*2] = -0.753\n",
    "\n",
    "# ==================================\n",
    "#  Spiral Path: high positive w, then small negative w\n",
    "# ==================================\n",
    "# w_data[:] = -1/100\n",
    "# w_data[0:100] = 1\n",
    "\n",
    "# ==================================\n",
    "#  Wave Path: square wave w input\n",
    "# ==================================\n",
    "#w_data[:] = 0\n",
    "#w_data[0:100] = 1\n",
    "#w_data[100:300] = -1\n",
    "#w_data[300:500] = 1\n",
    "#w_data[500:5700] = np.tile(w_data[100:500], 13)\n",
    "#w_data[5700:] = -1\n",
    "\n",
    "# ==================================\n",
    "#  Step through bicycle model\n",
    "# ==================================\n",
    "for i in range(t_data.shape[0]):\n",
    "    x_data[i] = model.xc\n",
    "    y_data[i] = model.yc\n",
    "    model.step(v_data[i], w_data[i])\n",
    "\n",
    "    x_solution[i] = solution_model.xc\n",
    "    y_solution[i] = solution_model.yc\n",
    "    solution_model.step(v_data[i], w_data[i])\n",
    "    \n",
    "plt.axis('equal')\n",
    "plt.plot(x_data, y_data,label='Learner Model')\n",
    "plt.plot(x_solution, y_solution,label='Solution Model')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We would now like the bicycle to travel a figure eight trajectory. Both circles in the figure eight have a radius of 8m and the path should complete in 30 seconds. The path begins at the bottom of the left circle and is shown in the figure below:\n",
    "\n",
    "![title](figure8.png)\n",
    "\n",
    "Determine the speed and steering rate inputs required to produce such trajectory and implement in the cell below. Make sure to also save your inputs into the arrays v_data and w_data, these will be used to grade your solution. The cell below also plots the trajectory generated by your own model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1085 -9.103679567619494\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYAAAAD8CAYAAAB+UHOxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvnQurowAAIABJREFUeJzt3Xd4VFX6wPHvmUnvPSE9dEKH0AQREREVxS7Y14KuZXWr7rp9dZvrFlfX7k8six3LioKVIjX0QIB00itJSJ3MzPn9kUERAyRkMvX9PE+ezNx7M+edJHPfe09VWmuEEEJ4H4OzAxBCCOEckgCEEMJLSQIQQggvJQlACCG8lCQAIYTwUpIAhBDCS0kCEEIILyUJQAghvJQkACGE8FI+zg7gZGJiYnR6erqzwxBCCLexbdu2Oq11bG+OdekEkJ6eTnZ2trPDEEIIt6GUKuntsVIFJIQQXkoSgBBCeClJAEII4aUkAQghhJeSBCCEEF5KEoAQQngpSQBCCOGlJAEIIYSXkgQghBBeShKAEEJ4KUkAQgjhpSQBCCGEl+r1ZHBKqReAhUCN1nqMbdvrwAjbIRFAo9Z6Qg8/WwwcASyAWWud1c+4hRBC9FNfZgN9EXgceOnoBq311UcfK6UeBZpO8vNna63r+hqgEEKIgdHrBKC1XquUSu9pn1JKAVcBc+0TlhBCiIFmrzaAM4FqrXXeCfZrYLVSaptSaqmdyhRCCNEP9loQZgmw/CT7Z2qtK5RSccAnSqn9Wuu1PR1oSxBLAVJTU+0UnhBCiOP1+w5AKeUDXAa8fqJjtNYVtu81wApg6kmOfUZrnaW1zoqN7dWqZkIIIU6DPaqA5gH7tdZlPe1USgUrpUKPPgbmAzl2KFcIIUQ/9KUb6HJgDhCjlCoDfqO1fh5YzHHVP0qpROA5rfUFQDyworudGB/gv1rrj+0Tvugvq1XTabbS0WWhw2zBoBRGg8LH0P09yM8Ho0E5O0whxADoSy+gJSfYflMP2yqAC2yPC4Hxpxmf6Ic2k5miulaK69ooqmuhvLGd2iOd1LaYqDvSSX1rJx1d1pO+hlIQFuBLeKAvEUG+xIb4kxQZSHJkIEkRQaRFBzE0LoQAX6OD3pUQwl7s1QgsnKyprYvd5Y3sLmsip7yJ3WVNlDe2f+uYmBA/YkMDiAnxY0hsMFFBfgT5+xDoayTQ14C/rxGtwWK10mXRmK1WWjotNLWZaGrv4nBbFxVNHWwpbuBIh/nr1zUaFOnRQYwcFEbmoDAmp0UyISVCkoIQLk4SgJtq7TSztbiBDQX1bCioY29FM1p370uPDmJSWiTXTEslIyaY9Ohg0mOCCPKz35+7qb2L8sPtFNW1cqCqmdyqI+wpa+LD3ZUA+BoVY5LCmZIexVnDY5mSHoWfj8w8IoQrUfroWcMFZWVl6ezsbGeH4TLqWjr5dF81H++tYkN+PSaLFT+jgUlpEcwYHENWeiRjEsMJD/J1WoyNbSa2HzrM1uLDZBc3sKu0CZPFSrCfkVnDYpg7Mo75mQlEBvs5LUYhPJlSaltvp9uRBODiWjrNrNxdydvby9ha3IBVQ0pUIOdlJjBnRByT0yIJ9HPdqpY2k5kN+fV8fqCGL/fXUNHUgY9BcdbwWC6ekMi5mfF2vTMRwttJAnBzWmu2FDXwenYpH+2por3LwuCYYC4an8h5oxMYNSgUW68qt6K1Zm9FMx/squD9XRVUNnUQ5Gdk0YRErpuexujEcGeHKITbkwTgpjq6LHywq4IXviomt7KZUH8fFo5P5IrJyUxKjXDLk/6JWK2arcUNvLWtjA92V9DRZWViagQ3zEhj4bhEfI3SXiDE6ZAE4GaaO7pY9lUxyzYWU9diYkR8KDfPSufi8UkuXb1jL01tXby1vYxXN5VQWNdKUkQgS2cP5uopKdKTSIg+kgTgJo50dPHiV8U8t76IpvYuzh4Ryy2zBjNzaLRHXe33ltaaLw7U8MQXBWwrOUxMiB+3njmYG2eke0UiFMIeJAG4OJPZyrINxTzxZT6NbV3MGxXHffOGMyZJ6sDhmzaQx7/IZ11eHQlhAfzo3OFcPjlZRiULcQqSAFyU1ppPc2t4+MN9FNe3MXt4LD8+dzjjUyKcHZrL2lxYz58+2s/O0kaGx4fwywszmT1cJgkU4kQkAbigwtoWfv3eXtbn1zEkNphfLcxkzog4Z4flFrTWfJxTxV8+3k9xfRsXjhvErxdmEh8W4OzQhHA5fUkA0gF7gJktVp5dV8Q/Pj1IgI+B316UybXT06SXSx8opTh/7CDmjorjmTWF/PuLfNYcqOVH5w7nxjPSpVpIiNMkdwADaG9FE/e/vZuc8mYWjE7g94tGEydXrf1WUt/Kr97by9qDtUxNj+LRq8aTEhXk7LCEcAl9uQOQy9ABYLVqnltXyCVPfEVVUydPXjuJp66fLCd/O0mLDmbZ96bw6JXjya1sZsE/1/L61kO48sWMEK5IqoDsrK6lk5+8uYsvD9RybmY8f718nMx7MwCUUlw+OZlpg6P46Zu7uf/tPXy+v4ZHrhxPWIDz5kISwp30+g5AKfWCUqpGKZVzzLbfKqXKlVI7bV8XnOBnFyilDiil8pVSD9gjcFe0paiBBf9cx4aCev6waDTPXD9ZTv4DLDkyiFdvncYvLhjJp7k1LHr8K/ZXNTs7LCHcQl+qgF4EFvSw/R9a6wm2r5XH71RKGYEngPOBTGCJUirzdIJ1Za9uLuGaZzcRGuDD+3fP5PoZ6V45mMsZDAbF0tlDWH7bdFo7zVzyxFes2NHjCqVCiGP0OgFordcCDadRxlQgX2tdqLU2Aa8Bi07jdVySyWzlwRV7eHBFDrOGxfDuXTMZmRDm7LC80tSMKP73g1mMT47gh6/v4m+rDki7gBAnYY9G4LuVUrttVUSRPexPAkqPeV5m2+b2WjrN3LJsK69uPsQdZw3h+RunEB4o9c/OFBcawCu3TmPxlBQe/yKfe1/bSUeXxdlhCeGS+psAngSGABOASuDRHo7pqR7khJdlSqmlSqlspVR2bW1tP8MbOLVHOlnyzCY2FNTzyBXjeOD8kdIf3UX4Gg386bKx/GzBCN7fVcH1z2+mqa3L2WEJ4XL6lQC01tVaa4vW2go8S3d1z/HKgJRjnicDFSd5zWe01lla66zYWNcc8n+ovo0rntpAXs0Rnr1hMldmpZz6h4RDKaW4c85Q/r1kIrtKm1jy7CbqWzqdHZYQLqVfCUApNeiYp5cCOT0cthUYppTKUEr5AYuB9/tTrjMV17Vy1dMbaWrv4r+3TWfuyHhnhyRO4qLxiTx7YxYFtS0sfmYTNc0dzg5JCJfR63EASqnlwBwgRilVBvwGmKOUmkB3lU4xcLvt2ETgOa31BVprs1LqbmAVYARe0Frvteu7cJCS+laWPLuJTrOF5bdNZ9Qgaex1B2cNj+XF703llmVbuerpjby2dAYJ4TIor7+sVk3Z4XYK61qoauqgurmTquYOao900Nxhps1kpq3TQqvJjMUKBgVGg8KgFP4+BsICfQkL9CU80JeoIF8SIwJJigwkKSKQlKggooP9pCfdAJOpIHqptKGNq5/eSFuXhf/eOp3MRDn5u5ttJYe58YUtDAoP4I3bZ8gYjT7o6LKwt6KZHYcOk1PeRF5NCwW1LXR0Wb91XHSwH3FhAYQF+BDs3/0V5GvEaFRYrRqr1lg1tHdZaG7vorm9i6b2LupbTRzpMH/ntUYOCmVkQhgjE0KZmBrJkNhgSQqnILOB2lldSyeXP7mBxrYu/nvbNFm71o1tLKjnxv/bwqiEUF69bToh/jIYviedZgvbig+zJq+WTYUN7KtoosvSfa5IDA9gWHwoQ+NCGBYXwuDYEBIjAogN9cff5/QX7mnu6KL8cDvlh9spaWjjYNUR9lc1c6D6yNeJJjrYj6z0SKakRzF7eCzD4kIkIRxHEoAdtZnMLHlmEweqj/Df26YzKbWnnq7CnXy6r5rbX9nG1PQoXrx5Sr9OWp7kcKuJj/dW8VluNRsK6mkzWfA1KiamRDIpLZKJqRFMTI0gLtSx1WcWq6aoroXs4sNsKW5ga3EDpQ3tAKREBXLOyHjmjYpn2uAomWUXSQB202WxsvSlbNYcrOXp67M4N1MafD3FuzvKue/1nVw2KYlHrxzvtVeRLZ1mVuVU8cHuCtbn1WG2alKiApkzPI6zhscyfUi0S94lVTS288WBGj7LreGr/Do6zVaigv24aNwgLp2UzPjkcK/9m8p6AHby0P/28cWBWh6+dIyc/D3MJROTKKlv4x+fHmRYXCjfnzPE2SE5VE55E69uPsR7O8tpM1lIigjkljMzuGhcIqMTw1z+5JkYEci109K4dloa7SYLa/NqeX9XBcu3lrJsYwmDY4K5ekoKV09JISJI2npORO4ATuDN7FJ++tZubpmVwa8WetzURYLulcZ+8NpO/re7gqeum8x5oxOcHdKAMlus/G93Jf+3oZhdpY0E+Bq4aFwii6emMCk10uVP+r3R3NHFx3uqeGt7GVuKGgjwNXDJhCRuPCPda3rtSRVQP+0ua+SKpzaSlRbJSzdPxUfqFT1WR5eFq5/ZRH71ET64ZxaDY0OcHZLddXRZeGtbGU+vLaC0oZ0hscFcNz2NyyYmEx7kuVOX5FY289LGYlbsKKejy8pZw2O5d94wj2/HkwTQD41tJi741zqUUnxwzyyipKugx6tobOeCx9YxKDyQFXeeQYCvZzQKm8xWlm85xONf5FN7pJPxKRHcNWcI80bFY/CiaUsa20y8uvkQz60r5HBbF2cOi+G+ecOYnBbl7NAGhCSA06S15vuvbOez/dW88/2ZjE2W7p7e4vP91dz8YjbXTEvlj5eOdXY4/aK1ZuWeKh5ZtZ/i+jamZURx7znDmDEk2iOqeU5Xa6eZlzeV8OzaQupbTSwYncDPLxhJWnSws0OzK2kEPk2vby3l471V/Pz8kXLy9zJzR8Zz+1mDeXpNITOHxHDhuEGn/iEXlFPexK/ey2HHoUaGx4fwfzdNYc6IWK8+8R8V7O/DHWcN4YYZaTy/rogn1xTw+d9ruGlmOnfPHeqVK8nJHYBNYW0LFz62nklpEbx88zSvukUW3bosVi5/cgNlh9tZ/cPZxIT4OzukXmvpNPPo6gMs21BMVLA/PztvBJdPTpYZak+iurmDv606wFvby4gO9uf3i0Zz/pgEt0+Wsih8H1mtmp++tRt/XwOPXjlBTv5eytdo4NErx9PSYeZX7+a4zWIyn+yrZt6ja3hxQzHXTEvlsx+fxVVTUuTkfwrxYQE8cuV43r9rFgnh/tz56nZuf3kb1V40YaAkAODVLYfYVnKYX16YKZOEeblh8aH88NzhfJRTxQe7K50dzkm1dpq5/63d3PZSNpHBfrzz/TN46JKxsihRH41NDufdO2fywPkjWXOwlnl/X8O7O8qdHZZDeH0CqGrq4C8f7Wfm0Ggun+QRC5WJfrrtzAzGp0Tw+w/20tzhmgvJbCs5zAWPreONbaXcOWcI7901k4ke3r1xIPkYDdxx1hA+vm82I+JDue/1nfzojZ20dppP/cNuzOsTwO8+2EuXxcrDl4x1+7o/YR8+RgMPLRpDfauJf36S5+xwvkVrzXPrCrnq6Y2YLZrXl87gZwtG4ufj9R9lu8iICea1pdP5wTnDeHdHOQv/vZ6c8iZnhzVgvPq/ZlNhPR/lVHH32UNJj/GsrmCif8Ymh3PN1FSWbSzmQNURZ4cDdE9MeM/yHTz0YS7zRsXx0X1nMjXDM/uyO5OP0cCPzh3Of2+bTrvJwuVPbuC9nZ5ZJdTrBGBb9L1GKZVzzLZHlFL7bYvCr1BKRZzgZ4uVUnuUUjuVUs6f35nuht+HPtxHYngAt80e7OxwhAv6yfwRhAb48Nv39zq9QfhQfRuXPrGBlXsquX/BSJ66brJXdlt0pOmDo/nwB7OYkBLBva/t5E8f5WKxukfHgN7qyx3Ai8CC47Z9AozRWo8DDgI/P8nPn621ntDb7kkDbcWOcnLKm/nZgpEeM/JT2FdksB8/Onc4GwvrWZtX57Q4dpU2ctmTX1F9pINlN0/l+3OGSHWlg0SH+PPKrdO4bnoqT68p5LaXsj2qXaDXCUBrvRZoOG7baq310d/GJroXfHd5nWYLj64+wPjkcC4en+jscIQLWzwlleTIQB5Ztd8pdwGf769m8TObCPQz8vb3z+DMYbEOj8Hb+RoNPHTJWB66ZAxrDtZyzXObaWg1OTssu7BnG8DNwEcn2KeB1UqpbUqppXYs87S8mV1GRVMHP54/Qvr8i5Py8zHww3nDySlv5uOcKoeW/UZ2Kbcuy2ZoXAhvf/8MhnjgRHXu5LrpaTx13WRyK5u58qkNVDS2OzukfrNLAlBKPQiYgVdPcMhMrfUk4HzgLqXU7JO81lKlVLZSKru2ttYe4X2LyWzlyS8LmJgawZnDYuz++sLzXDIxiWFxIfz9k4NYHVQHvHzLIX721m5mDo3htaXTHb4Kl+jZuZnxvHzzVGqaO7niyQ0U17U6O6R+6XcCUErdCCwErtUnuEfWWlfYvtcAK4CpJ3o9rfUzWussrXVWbKz9b3ff3l5GeWM7954zTOpRRa8YDYq7zh5KXk0LXxyoGfDyXt1cws/f2cOcEbE8e0MWwS64Ipc3mzY4mtdun057l4Vrnt1EaUObs0M6bf1KAEqpBcD9wMVa6x5/C0qpYKVU6NHHwHwgp6djB5rVqnlmbSHjk8M5a7jUpYreu3DcIBLDA3h6beGAlrN8yyEeXJHD3JFxPH39ZOmg4KJGJ4bz8i3TaOk0c81zm9y2Oqgv3UCXAxuBEUqpMqXULcDjQCjwia2L51O2YxOVUittPxoPrFdK7QK2AB9qrT+267vopTV5tRTVtXLzrAy5+hd94ms0cPOsDLYUNbCztHFAyvg4p4oHV3Rf+T953SRZrN7FjUnqTgKNrV1c+9xm6lo6nR1Sn3nVbKA3vrCF3Mpm1t8/V0ZOij5r6TRzxp8+Y86IOB5bMtGur725sJ7rX9jC6MQwXr11GkF+Uu3jLraVHOba5zYxMiGM5bdNJ9DPuYlbZgPtQUFtC2sO1nLd9DQ5+YvTEuLvw2WTkvk4p4rDduwGeLD6CLe+lE1KZCAv3DhFTv5uZnJaJI8tnsiuskbufW2HWw0W85oz4RtbS/ExKJZMTXV2KMKNXT0lBZPFyjt2mi2ysc3ErcuyCfA18tIt04iUJUjd0vzRCfx6YSar91Xz8Ie5zg6n17wiAVismhU7ypkzIo7YUPdZ5EO4nlGDwhifEsFrWw71e2CYxaq5Z/kOqpo6ePr6ySRFBNopSuEM35uZwU1npPPCV0VuM520VySAr/LrqDnSKdM9C7tYMiWFvJoWdpf1b5bIv67az7q8On6/aDSTZCpnj/DghaOYmh7Fz9/Z4zKTCJ6MVySAd7aXERbgw9xRcc4ORXiABWMS8DEoVu45/QVjPsut5uk1hVw3PZXFUi3pMXyNBh6/ZiIhAT7c8co2l11P4iiPTwCdZguf7KvmgrGDpFudsIuIID9mDYvhwz2Vp1UNVNPcwU/f2s2oQWH8amHmAEQonCkuLIAnrpnEoYY2fv2uU4Y89ZrHJ4CNBfW0mizMHx3v7FCEB7lg7CDKDrf3uRrIatX8+M1dtHaaeWzxBLko8VBTM6K4Z+5Q3t1ZwYcuvLSoxyeAT/ZVE+Rn5IwhMu+PsJ/zMhMwGhSr9vZtgriXNhazLq+OXy7MZFh86MAEJ1zCXWcPZXxyOL98dw81LrrQvEcnAK01n+ZWM3tYrAypF3YVHuTLpNQI1vVhnYDyxnb+uuoAZw2P5bppUu/v6XyNBh69agJtJgs/f2eP0xcV6olHJ4CD1S1UN3dK468YELOHxZJT0UR9L6YA0Frzq3dz0BoeumSMTEXiJYbGhfDT80bw2f6aPt8tOoJHJ4CNBd1XZzMGRzs5EuGJzhwei9awPv/UdwEf7qnk8/01/Hj+cFKighwQnXAVN52RzsiEUH73wT6XW03MoxPApsIGkiMD5QMnBsTYpHDCA33ZkF9/0uPaTGb+8L99jEkK46Yz0h0TnHAZPkYDD186hsqmDh77LM/Z4XyLxyYAq1Wzuaie6XL1LwaI0aCYlBrBjtLDJz3u2bVFVDd38tuLRuNj9NiPnDiJyWlRXJWVzPPriyhyoUVkPPa/sai+lcNtXUxNj3J2KMKDTUyNJK+m5YQDfmqaO3h6bQHnj0kgS/4XvdpPzhuBr9HA31YfcHYoX/PYBJBT3t0/e0xSuJMjEZ5sYmoEWsPu0p7HA/zj04N0Wazcv2CkgyMTriYuNIBbz8zgw92V7OnnNCL24rEJYF9FM35GA8PiZSFtMXDGp0QAsKvsu4vElDa08UZ2GddOSyM9JtjRoQkXtHT2YCKDfPnrqv3ODgXo24pgLyilapRSOcdsi1JKfaKUyrN973FGK6XUAqXUAaVUvlLqAXsEfio5FU2MSAjFV+pcxQAKC/AlKSKQvOrvTvz15JoCjEpxx1lDnBCZcEWhAb7cOWco6/Lq2FZy8rYjR+jL2fFFYMFx2x4APtNaDwM+sz3/FqWUEXgCOB/IBJYopQZ8ApT9lUfIHBQ20MUIwdC4EPJqWr61rbKpnbeyy7gyK5mE8AAnRSZc0TXTUgkP9OXpNQXODqX3CUBrvRZoOG7zImCZ7fEy4JIefnQqkK+1LtRam4DXbD83YJo7uqhvNZERK7fdYuANiwuhoLYF6zErQT2zthCr1nL1L74j2N+HG2ek8UluNfnHXTg4Wn/rR+K11pUAtu89DblNAkqPeV5m29YjpdRSpVS2Uiq7trb2tII6VN8GQJr0/xcOMDQuhI4uK+WN7UD32sFvZpexcNwgGYMienTjGen4+xh4Zq1z7wIcUUHe05j3E06KobV+RmudpbXOio2NPa0CS44mgGi5AxAD7+hJ/mgCWLG9jJZOMzfKoC9xAtEh/lw+KZn3dlbQ1Oa8NQP6mwCqlVKDAGzfa3o4pgxIOeZ5MlDRz3JP6lBDdwJIjZarLzHwjtbxVzV1oLVm2cYSxiWHM8HWQ0iIniyZmkqn2cqKHWVOi6G/CeB94Ebb4xuB93o4ZiswTCmVoZTyAxbbfm7A1LV0EuRnJMTfZyCLEQKAhDBbAmjuYHdZE/k1LVwzNVUmfBMnNSYpnHHJ4SzfUuq0mUL70g10ObARGKGUKlNK3QL8GThXKZUHnGt7jlIqUSm1EkBrbQbuBlYBucAbWuu99n0b31bf0kl0iN9AFiHE1wJtU423myys3FOJj0GxYEyCk6MS7mDJ1FQOVB9h+6HvjiNxhF5fImutl5xg1zk9HFsBXHDM85XAyj5Hd5rqW01EB/s7qjjh5QwGha9RYbJYWb2vmplDY4gIkgsQcWoXjU/kt+/v5YNdFUxO63EY1YDyyFFS9S0mooPlAygcR6Foau+iqK6VqRky54/onRB/H+aMiGXlnspvdSN2FI9MAO1dFoKl/l84SJfFislipaS+e5ZHmX9K9MUFYwdRc6STbCeMDPbIBNDZZcHfxyPfmnBBbZ0WAIpquxPA6EQZgS5675xR8fj7GFi5x/GLx3vkWbLTbMXf1yPfmnBBTe3d/bgrmjpICAsgJkTan0Tvhfj7MGtoDF8c6KkX/cDyyLNkp9mKn1EWgReOUdf6zZrAY5Lk6l/03ezhsZTUt309i4GjeGQC0FojXbCFo9Qd+SYBZCZK/b/ou1nDYgBYl39609+cLo9MAL4+BswWq7PDEF6ivtX09eMxUv8vTsPgmGCSIgJZd7DOoeV6ZgIwGjBZnDOyTnifssPf3LaPlh5A4jQopZg+OJrskgaHjgr2yATgZzTQJXcAwkEKarp7/0QG+ZIoc/+L0zQhNYK6FhNlh9sdVqZHJgB/XwNtJrOzwxBeoqC2e073MUnhMv+POG0TT7K86EDxyAQQFeTH4VbnTbEqvIfZYv16NbBMqf8X/TAiIRQ/HwM7HTgvkEcmgMhgPw63mU59oBD9VHrM7foY6QEk+sHXaGDUoDD2VTY7rEzPTABBvpIAhEMU1X2zpJ9MASH6a0hsMIW2EeWO4JEJIDrEn4ZWk1MmVxLepajumx5AsgSp6K8hsSFUNXfQ0umYNkyPTADJkYF0WTTVRzqcHYrwcMV13VdrU9IjMRikAVj0z5DY7mVsixx0F9DvBKCUGqGU2nnMV7NS6r7jjpmjlGo65phf97fck0mJ7L4Sc/SwauF9Cuu+6QEkRH9lxIQAUFzvmATQ7zmTtdYHgAkASikjUA6s6OHQdVrrhf0trzdSbbfipYfbmeaIAoXX+iq/HoDR0gAs7CA+rHsiwZpjphcZSPauAjoHKNBal9j5dfskMSIQg+Lr+dmFGGhHb92F6I/wQF/8jAZqHFR9be8EsBhYfoJ9M5RSu5RSHymlRtu53G/x8zEwODaE3MojA1mM8HLHjjZPigx0YiTCUyiliA31p7bZze4AlFJ+wMXAmz3s3g6kaa3HA/8G3j3J6yxVSmUrpbJra09/ZrxRg8LIdWB/WuF9Go6ZBC5G1qAWdhIT6k9ti5slAOB8YLvWuvr4HVrrZq11i+3xSsBXKRXT04torZ/RWmdprbNiY2NPO5jMQWGUN7bT1CYjgsXAaDzmf0t6AAl7CfE30mayOKQseyaAJZyg+kcplaBsk6Qopabayq23Y9nfcXRY/t6KpoEsRnixTrNjPqTCuwT6+tDuTglAKRUEnAu8c8y2O5RSd9ieXgHkKKV2AY8Bi/UAz3k6ITkCpWCbExZaFt6h09zdBpAs9f/CjgL9jHR0OSYB9LsbKIDWug2IPm7bU8c8fhx43B5l9VZ4kC8j4kPZUtzgyGKFFzlavTgkNsTJkQhPEuhrcMsqIJczLSOKbSWHZXUwMSCODtbJiJEuoMI9eXQCmJoRTZvJwp5yaQcQ9lfV1N1XOy5MegAJ+zFbNT5Gx3Qq8OgEMGNINAYFXx5w7ELLwjtU2hJAYri0AQj7sVg1Pg7qVebRCSAq2I9JqZF8tv87PVOF6Lfyxu61AMKDfJ0cifAkZovGKAnAPs4ZFU9OefPXt+tC2EtlU3cCMJmljUnYT6vJTKCf0SFleXwCmDcqDoBPc+UuQNjX0WVHZbChsKd4zA1zAAAdiElEQVTGti4ig/wcUpbHJ4ChcSEMjg3mg10Vzg5FeJCWTjMmW++y+lZZfU7YT1N7FxGSAOxDKcWlE5LYXNTwdZ2tEP21r+KbeaYaWh0zb4vwDofbTEQ6qF3J4xMAwKIJSQC8t7PcyZEIT3G0a7GvUVHfIncAwj46zRaa2ruICpY7ALtJjQ4iKy2SFdvLGeAZKISX2FPWSFyoP+OTI+TOUthN+eF2tP5mVcOB5hUJAODKrGTyalrYUiRTQ4j+0VqzuaiBrPRIUqODKJGlR4WdHGro/l9KiZIEYFcXj08iPNCXlzY6dbEy4QGK69uobOrgjCExpEcHU9Xc4bDJu4RnKz3cfTeZKgnAvgL9jFw9JYVVe6tkTIDolw0FdQCcMSSatOjuD+rRKzch+qO4rhV/HwNxoY6ZXsRrEgDAddPSsGjNK5vkLkCcvg359QwKDyAjJvjrmUAPVMnyo6L/ciubGZkQ6rAFhrwqAaRGB3FeZgLLNhbT3CGDd0TfdZotrDlYy+xhsSilGB4fip/RQI4sPCT6SWvNvsrmrxezcgR7LQhTrJTao5TaqZTK7mG/Uko9ppTKV0rtVkpNske5p+PuuUM50mHmpQ3FzgpBuLEN+fW0dJpZMDYBAD8fAyMSQtlbLutPi/6pbOqgsa2LzEFulgBsztZaT9BaZ/Ww73xgmO1rKfCkHcvtkzFJ4cwdGcfz64to7TQ7KwzhplbtrSLE34czhnyz/tGYpDByKpqki7Hol6NjS9zuDqAXFgEv6W6bgAil1CAHlf0d98wdyuG2Ll6UuwDRB2aLlU/2VTN3ZBz+Pt9M1jU+OYLGti4KaludGJ1wd1uKGvD3MTA6MdxhZdorAWhgtVJqm1JqaQ/7k4DSY56X2bY5xcTUSM7NjOfJLwuoa5Fh/KJ31hyspb7VxMJx3752mT64+25gY2G9M8ISHmJTYT0TUyMI8HXMTKBgvwQwU2s9ie6qnruUUrOP299Tk3aP98tKqaVKqWylVHZt7cAt5PLA+SNp77Lwr0/zBqwM4VneyC4lJsSPs0fGfWt7WnQQg8ID2FQgCUCcnqb2LvZVNjMtI/rUB9uRXRKA1rrC9r0GWAFMPe6QMiDlmOfJQI/Tc2qtn9FaZ2mts2JjY+0RXo+GxIZwzdRU/rvlEPk1LQNWjvAMtUc6+Sy3hssmJeNr/PbHRinFjCHRbCysx2qVdgDRd1uKGtAapg2Ocmi5/U4ASqlgpVTo0cfAfCDnuMPeB26w9QaaDjRprSv7W3Z/3TtvGEG+Rn7zfo404ImTemd7GWar5srJyT3unzkkhoZWk6w/LU7LZ7nVhPj7MDkt0qHl2uMOIB5Yr5TaBWwBPtRaf6yUukMpdYftmJVAIZAPPAvcaYdy+y0mxJ+fnT+Sr/LreVdmChUnYLZYeWljCVPToxgWH9rjMXNHxmE0KFbtrXJwdMLdWa2aT3NrOGtE7Lc6FziCT39fQGtdCIzvYftTxzzWwF39LWsgXDs1lbe3lfGH/+UyZ3gckQ6ahlW4j5U5VZQ3tvObizJPeExksB/TMqJYtbeKny0Y6cDohLvbUdpIXUsn8zPjHV62V40E7onBoPjTZWNpbu/iDx/uc3Y4wsVorXluXSEZMcHMG3XyD+h5oxMoqG2VNiXRJ6v3VuFjUMwZHnfqg+3M6xMAwKhBYXx/zhDe2V7Oyj1Ob5oQLmRjYT27y5q4eVbGKednOW90AkrB+7L8qOgli1Xz7s5yzhoeS7iDVgE7liQAmx+cM4zxyeH8YsUemS1UAN1X/39ffZD4MP8TNv4eKyE8gFlDY3h7W5n0BhK98lV+HdXNnVzei/+vgSAJwMbXaOAfV0+gs8vKT9/aJR9gwZcHa8kuOczdc4f1enDOlVkplDe2y6Aw0Stvby8jLMCHuSMdX/0DkgC+ZXBsCL++KJN1eXX8+/N8Z4cjnEhrzaOrD5AcGcjVWSmn/gGb+ZnxhAX48EZ26akPFl6tsc3Eqr1VXDQ+0aGjf48lCeA4i6ekcNnEJP752UG+OFDj7HCEk7y/q4Kc8mbumzccP5/ef0wCfI1cMjGJj/ZUUXtEphkRJ/ba1lI6uqxcOy3NaTFIAjiOUoqHLx3LqIQw7l2+g0Oy3qvXaek088eVuYxNCufSiX2fsuqmM9Lpslp5WRYeEidgtlh5aUMx0wdHOXT2z+NJAuhBoJ+Rp6+fjFKKW1/aSlO7LB7jTf79eR7VzZ38btFojKexMtPg2BDOGRnPK5tKZK1g0aNVe6upaOrg5pkZTo1DEsAJpEQF8eS1kyiqa+WOl7dhMludHZJwgPyaFl5YX8SVk5OZlHr6w/JvPTODhlYT72yXEebi27TWPLO2gNSoIM45xdiSgSYJ4CTOGBrDX68Yx8bCeu5/e7fMF+ThLFbNz97aRZCfT79H807LiGJ8cjj/+TJfLh7Et3xxoIZdZU3cOWfIad1h2pMkgFO4dGIyP5k/nBU7ynn4w1xJAh7s+fWFbD/UyO8uHk1sqH+/XkspxQ/PHU7Z4XbpESS+prXmn5/mkRIV6LS+/8eSBNALd509lBtnpPHc+iIeWXVAkoAHyq85wt9WH2R+ZjyLJiTa5TXPGh5LVlok//48T9oCBACf5dawu6yJe84e9p1pxZ3B+RG4AaUUv7loNEumpvKfLwv4pywi41E6uizc9/pOgv2MPHzpWJSyz225Uoofzx9BdXMnL2+UHkHersti5S8f7yc9OohLJzltQcRvkQTQSwaD4uFLxnDl5GT+9Vkej66WOwFP8fCHueSUN/OXy8f1u+rneDOGRDNnRCyPfZYn4wK83KubSsiraeHBCzNd4uofJAH0icGg+PPl47g6K4V/f57PL9/NwSJTRri1D3ZV8PKmEm47M4P5oxMGpIxfL8ykw2zhLx/vH5DXF66vodXE3z85yJnDYpg3yjnTPvTEHiuCpSilvlBK5Sql9iql7u3hmDlKqSal1E7b16/7W66zGA2KP18+ljvOGsKrmw/xg+U76DRL/a47yq85wgNv72ZSasSAzuE/ODaEm2dl8Na2MrYfOjxg5QjX9ejqA7SaLPxqYabdqhjtwR53AGbgx1rrUcB0uheF72nljHVa6wm2r9/boVynUUrxwPkjefCCUXy4p5Lrn99CQ6vJ2WGJPqhv6eR7L24l0M/I49dMGvBb8nvmDiM+zJ8HV+RIt1Avs7mwnlc3H+LGGekMP8GKcs7S7/96rXWl1nq77fERIBdwjRaOAXbb7MH8a/EEdpY2cvHj69lf1ezskEQvdHRZuP3lbdQ0d/LsDVkkRgQOeJkh/j48dMlYciubeeILmWjQW7SbLNz/9m5So4L4yXnDnR3Od9j1skcplQ5MBDb3sHuGUmqXUuojpdRoe5brTIsmJPHG7TMwma1c/p8Nsiasi7NaNfe/vZvsksM8etV4JvZjtG9fnZsZz6UTk3jii3z2Vsji8d7g758coLi+jT9fNpYgv36vwGt3dksASqkQ4G3gPq318ZfC24E0rfV44N/Auyd5naVKqWylVHZtba29whtQE1IieP/uWQyJC+H2l7fx+w/2SbuAC9Ja87sP9vLezgp+et4IFo6zT3//vvjNRZlEBvvx4zd2ydgAD7ehoI7n1hexZGoqZwyNcXY4PbJLAlBK+dJ98n9Va/3O8fu11s1a6xbb45WAr1Kqx9+I1voZrXWW1jorNjbWHuE5REJ4AG/cPoMbZ6TxwldFXPHkRkrqW50dljjGX1cdYNnG7h4/d84Z4pQYIoL8+MvlY9lfdYSHZA1qj1XX0sl9r+0kIyaYX144ytnhnJA9egEp4HkgV2v99xMck2A7DqXUVFu5HrdkUoCvkd8tGsNT102mpL6VCx9bz/Ith2S8gAt4/PM8nvyygGunpfKLC0Y5tSfG3JHxLJ09mFc2HeIDWT/Y41itmh+/sYvG9i4eXzKJYH/Xq/o5yh53ADOB64G5x3TzvEApdYdS6g7bMVcAOUqpXcBjwGLtwWfFBWMSWHnvmYxJCuPn7+zhuuc3U9og6wo4g9aaR1bt52+rD3LZxCT+sGiMS3TD++l5I5iUGsEDb++msLbF2eEIO3pyTQFrDtbyqwtHOXWu/95QrnwezsrK0tnZ2c4O47RZrZr/bjnEn1bmooGfzB/BDTPS8HGRUYCezmrV/PaDvby0sYQlU1N56JIxTp998VgVje1c+Ng6ooL9eOfOmYQH+jo7JNFPq/dWcfsr21g4LpHHFk9wysWGUmqb1jqrN8fKmWgAGQyK66ansfpHZzElPYrf/28fFzy2jq/y65wdmsczma38+M1dvLSxhNtnD+aPl7rWyR8gMSKQJ6+bzKGGNu7+73a6LDI+wJ3lVjZz3+s7GZcUziNXjHOJO81TkQTgAEkRgbz4vSk8ff1k2rssXPvcZu54eRtFddJIPBAaWk1c99xmVuwo56fnjeCB80e67Idx+uBoHr50LOvy6vjt+3ulvchN1Rzp4NZl2YQG+PDMDVlOW+S9r1y3dcLDKKU4b3QCZw2P5bl1hTzxRQGf5FZz+aQk7pk7jJSoIGeH6BHyqo9w87KtVDd38tiSiVw83vFdPfvqqqwUCmpbeHpNIYPCA7h77jBnhyT6oKmtixue38LhNhOvLZ1OfFiAs0PqNUkADhbga+TuucO4akoKT35ZwKubD7FiRzlXZaWwdPZg0qKDnR2i2/o4p5Kfvrkbf18jry+d7tBBXv11/3kjqWnu5G+rDxLi78NNTl4rVvROm8nMzcu2Uljbygs3TWFccoSzQ+oTaQR2ssqmdh7/PJ83sksxWzXnZSZw2+wMJqdFOTs0t9FptvDHD3NZtrGkexnG6yaT5IDpHezNbLFy56vbWb2vmkeuGMeVWSnODkmcREeXhaUvb2N9Xi3/uXYSC8YMcnZIQN8agSUBuIjq5g5e2ljMK5sO0dTexfiUCBZPSWHhuEGEBkjvkBMpqmvlnuXbySlv5pZZGdy/YCR+Pu7btNVptnDrsmy+yq/jL5dLEnBV7SYLS1/OZl1eHX+9fBxXTXGdv5MkADfWZjLz1rYyXtlUwsHqFgJ9jVw4bhCXT0pmakaUy/VkcRaLVfPihmIeWbUffx8jf7tyPOdmxjs7LLtoM5m5/eVt3Q3DF2VKdZCLOdLRxS0vZpNd0sBfrxjPFS6wtu+xJAF4AK01O0sbeSO7lA92VdLSaSYmxI/5oxM4f0wC0wdHu8yqQo5WWNvCz97qntBt7sg4/njpWBLC3afhrTc6zRZ+sHwHq/ZW85P5w7nr7KEu25PJm9S3dHLzsmxyypv459UTuMgFOxlIAvAwbSYzn++v4aOcKr7YX0ObyUJogA8zBkcza1gMM4fGMDgm2ONPEG0mM099WcBTawsJ9DXym4syuXRikse+b7PFys/e2s07O8q5dloqv714tNcmfVdQUNvCzS9upbKpg8eXTBywFeT6qy8JQHoBuYEgPx8Wjktk4bhEOrosrD1YyxcHaliXV8fqfdUAxIf5MyElgvEpEYxPjmBscjhhHtJ2oLXmf7sr+ePKXCqbOlg0IZEHLxhFnBt1tzsdPkYDf7tyPPHhATz5ZQEl9W08ce0kGTHsBBsL6rnjlW34GBTLb5vO5DT36WF2MnIH4Ma01hxqaGN9fh2bCxvYXdZIcf03cw7Fh/kzOCaEIXHBZMSEkBgeQFyYP3Gh3d/9fXo3WEVrTXuXhcNtXVQ1tVPR2EFlUzsNrV08cP7ALaUIsCG/jkc/Oci2ksOMTgzjtxePZkq69/WQejO7lF+s2ENKVBDP3ZDF4NgQZ4fkFbTWvLr5EL/7YC+pUUH8301TSY127TE7UgXkxRrbTOwuayKnoomCmlYK61ooqGmhucP8nWMDfA0E+fkQ5Gck2M8Ho0Gh6f6nt2qNyWylucNMc3sXZut3/09C/H3Y9qt5vU4kfbGlqIG/f3KATYUNJIQFcO+8YVyVleLVjeCbC7uvQk1mK3+6fJxbDHJzZ20mM794Zw/v7qxg9vBY/r14IuFBrn/3JQlAfIvW2nb13kHNkQ5qmjupbu6gpdNMq8lMW6eFVpMZi1WjlMKgwKAUvkYDYYE+hAX4EhrgS0SQLwnhASSGBzIoIsDuVUwWq+bT3GqeX1/ElqIGYkL8uevsISyZmuo2Q+sHWkVjO/cs38G2ksNcOy2VXy3MlN/NAMirPsKdr26noLaFH87rboQ3uMnFhyQA4Vaa2rt4Z3sZ//dVMYca2kiKCOR7M9O5dloagX5ycjtel8XK31Yf4Ok1hYxMCOVvV45nTFK4s8PyCFar5oWvinhk1QFCA3z41+KJzHTR1bxORBKAcHkWq2Z9fh1vbStj1d4qTGYrk9MiuWVWBvMz42XK7F744kAN97+1m/pWE3fNGcLdc4e59SA4Zyupb+Wnb+5mS3ED80bF88fLxhAX6n4dDRyeAJRSC4B/AUbgOa31n4/br2z7LwDagJu01ttP9bqSADxLl8XK1qIGVu+r5uOcKqqaO4gI8mXR+ESuzEqRq9jT0NTWxe/+t5d3tpczMiGUhy8d6zE9VBzFZLbywldF/OvTPHwMit9cPJrLJ7lv92KHJgCllBE4CJwLlAFbgSVa633HHHMBcA/dCWAa8C+t9bRTvbYkAPdX2dTOxoJ61ufV8dn+Gprau/D3MTB7eCyXTUxi7qi4AWlE9jaf7qvmwXf3UN3cyWWTknhgwUiP7yZrD+vz6vjN+zkU1LYyb1Q8v180mkQ3nEfqWI4eBzAVyNdaF9oKfw1YBBy74vUi4CXbMpCblFIRSqlBWutKO5QvXESn2cLBqhZyKprYVdrIxsJ6SmzdUiOCfDlnVBzzMxOYPTyGID8ZgmJP8zLjmTEkmie+yOe5dUWs3lvN3XOHctMZ6dJI3IP8miP8bdVBPt5bRWpUEC/clMXckZ4xlUhf2ONTmASUHvO8jO6r/FMdkwRIAnBDj32WR3FdK51mK51mC/WtJlsPo04stu6iYQE+TM2I5oYZ6UwfHMWohDC36UXhroL9ffjZgpFclZXCH/63jz9/tJ8X1hdx19lDWTw1Re60gLLDbfzr0zze3l5GoK+RH507nKWzB3ttkrRHAujpU318vVJvjuk+UKmlwFKA1NTU/kUmBsTO0kbyao7g72PEz2ggKtiPM4bEkBgRwKhBYYxODCMlMkhO+E6SHhPM8zdNYXNhPY+uPshv3t/L02sK+P7ZQ7liUrJX9qwqrG3hufVFvJVdBgpunpnB9+cMITrE39mhOZU92gBmAL/VWp9ne/5zAK31n4455mngS631ctvzA8CcU1UBSRuAEP2jdXdvq0dXH2RnaSMRQb5cNy2NG2akeXwbgdaabSWHeXptIZ/mVuNrNHDF5GTuPnuo29fzn4yjG4F96G4EPgcop7sR+Bqt9d5jjrkQuJtvGoEf01pPPdVrSwIQwj601mwtPsxz6wr5JLcaH4NiwZhBXDk5mZlDYzxqhHVjm4kVO8p5fWsp+6uOEBHkyw3T07jhjHRivOCK36GNwFprs1LqbmAV3d1AX9Ba71VK3WHb/xSwku6Tfz7d3UC/199yhRC9p5RiakYUUzOiKK5r5cUNxazYUc4HuyoYFB7A5ZOSuXhCIsPiQtyy+2NHl4V1eXW8v6vi63ElY5PCeeiSMVw2KUk6HZyADAQTwkt1dFn4LLeGN7eVsvZgLVYNGTHBzB8dz/zMBCamRLh0O05Texfr8+r4KKeSL/bX0GqyEB7oyyUTErlqSgqjE71zXImMBBZC9ElNcwer91Wzam8VGwvqMVs1EUG+TMuIYsbgaGYMiWF4vHPvDlo7zewqbeSrgjrW59ezp6wRq4bo4G8WSpoxxHsXSjpKEoAQ4rQ1tXfx5YEavsqvY2NhPaUN7QCEBvgwOjGMMYnhjEkKZ3h8KGnRQQT727d6RWtNdXMnRXWt5NUcYVdpE3vKG8mvacGqwWhQTEiJYObQGGYNjWFyWqRHtWH0lyQAIYTdlDa0sbGwnt1ljeSUN5Nb2Uyn2fr1/pgQf9Kig0iODCQq2I+oID+iQvyICPTD38eAr48BX6PCz2jAZLF2jx/pstDRZaWxzUR9q4m6lk5qj5gob2ynpL6VNpPlmNf3Y1xyBGOTwpmQEkFWeiShHrLY0UCQFcGEEHaTEhVESlQQV2WlAN1LVebXtpBf00JJfRuH6tsoaWhlx6FGGlpNtHR+d+2JkzEoiA7xJzrYj0HhAcwYHE1GTBAZtsWMEsIC3LJh2h1IAhBC9ImP0cDIhDBGJoT1uL/TbOFwaxeN7Sa6zBqTxYrJbMVsteJrNODvY8Dfx4i/r4GIQF8ig/xcurHZk0kCEELYlb+PkYRwIwnhnj3QzBN4d3O5EEJ4MUkAQgjhpSQBCCGEl5IEIIQQXkoSgBBCeClJAEII4aUkAQghhJeSBCCEEF5KEoAQQngpSQBCCOGl+jUVhFLqEeAiwAQUAN/TWjf2cFwxcASwAObezlQnhBBi4PT3DuATYIzWehzd6wL//CTHnq21niAnfyGEcA39SgBa69Va66Nzv24CkvsfkhBCCEewZxvAzcBHJ9ingdVKqW1KqaUnexGl1FKlVLZSKru2ttaO4QkhhDjWKdsAlFKfAgk97HpQa/2e7ZgHATPw6gleZqbWukIpFQd8opTar7Ve29OBWutngGege0WwXrwHIYQQp+GUCUBrPe9k+5VSNwILgXP0CdaX1FpX2L7XKKVWAFOBHhOAEEIIx+hXFZBSagFwP3Cx1rrtBMcEK6VCjz4G5gM5/SlXCCFE//W3DeBxIJTuap2dSqmnAJRSiUqplbZj4oH1SqldwBbgQ631x/0sVwghRD/1axyA1nroCbZXABfYHhcC4/tTjhBCCPuTkcBCCOGl1AnabV2CUqoWKOlhVwxQ5+Bw7M3d34PE73zu/h7cPX5wzfeQprWO7c2BLp0ATkQple3uI4rd/T1I/M7n7u/B3eMH938PUgUkhBBeShKAEEJ4KXdNAM84OwA7cPf3IPE7n7u/B3ePH9z8PbhlG4AQQoj+c9c7ACGEEP3kVglAKXWlUmqvUsqqlMo6bt/PlVL5SqkDSqnznBVjbymlfquUKreNoN6plLrA2TH1hlJqge13nK+UesDZ8ZwOpVSxUmqP7fee7ex4ekMp9YJSqkYplXPMtiil1CdKqTzb90hnxngyJ4jfbT4DSqkUpdQXSqlc2znoXtt2t/kb9MStEgDdcwhdxnETySmlMoHFwGhgAfAfpZTR8eH12T9si+RM0FqvPPXhzmX7nT4BnA9kAktsv3t35G4LFL1I9//2sR4APtNaDwM+sz13VS/y3fjBfT4DZuDHWutRwHTgLtv/vjv9Db7DrRKA1jpXa32gh12LgNe01p1a6yIgn+4ZR4V9TQXytdaFWmsT8Brdv3sxwGzTpzcct3kRsMz2eBlwiUOD6oMTxO82tNaVWuvttsdHgFwgCTf6G/TErRLASSQBpcc8L7Ntc3V3K6V2226P3eHW0V1/z8fr9QJFLi5ea10J3ScoIM7J8ZwOd/sMoJRKByYCm3Hzv4HLJQCl1KdKqZwevk52pal62Ob07k2neC9PAkOACUAl8KhTg+0dl/w9n4aZWutJdFdl3aWUmu3sgLyU230GlFIhwNvAfVrrZmfH01/9mg10IJxqAZoTKANSjnmeDFTYJ6LT19v3opR6FvjfAIdjDy75e+4rD1qgqFopNUhrXamUGgTUODugvtBaVx997A6fAaWUL90n/1e11u/YNrv138Dl7gBO0/vAYqWUv1IqAxhG99oDLsv2z3LUpbjHIjlbgWFKqQyllB/dDe/vOzmmPvGwBYreB260Pb4ReM+JsfSZO30GlFIKeB7I1Vr//Zhd7v03cKeBYEqpS4F/A7FAI7BTa32ebd+DdC9Mb6b79uxEC9S7BKXUy3Tf+mqgGLj9aF2iK7N11fsnYARe0Fo/7OSQ+kQpNRhYYXvqA/zXHd6DUmo5MIfu2Sergd8A7wJvAKnAIeBKrbVLNrSeIP45uMlnQCk1C1gH7AGsts2/oLsdwC3+Bj1xqwQghBDCfjylCkgIIUQfSQIQQggvJQlACCG8lCQAIYTwUpIAhBDCS0kCEEIILyUJQAghvJQkACGE8FL/D4/RoHOH/iv8AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample_time = 0.01\n",
    "time_end = 30\n",
    "model.reset()\n",
    "\n",
    "t_data = np.arange(0,time_end,sample_time)\n",
    "x_data = np.zeros_like(t_data)\n",
    "y_data = np.zeros_like(t_data)\n",
    "v_data = np.zeros_like(t_data)\n",
    "w_data = np.zeros_like(t_data)\n",
    "\n",
    "v_data[:] = 16 * np.pi / 15\n",
    "w_data[:] = 0\n",
    "w_data[:21] = model.w_max\n",
    "w_data[318:338] = -model.w_max\n",
    "w_data[380:402] = -model.w_max\n",
    "w_data[1804:1824] = model.w_max\n",
    "w_data[1830:1851] = model.w_max\n",
    "\n",
    "# ==================================\n",
    "#  Learner solution begins here\n",
    "# ==================================\n",
    "for i in range(t_data.shape[0]):\n",
    "    x_data[i] = model.xc\n",
    "    y_data[i] = model.yc \n",
    "\n",
    "    \n",
    "    model.step(v_data[i], w_data[i])\n",
    "print(np.argmin(x_data[1500:]), np.min(x_data[1500:]))    \n",
    "# ==================================\n",
    "#  Learner solution ends here\n",
    "# ==================================\n",
    "plt.axis('equal')\n",
    "plt.plot(x_data, y_data)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will now run your speed and angular rate inputs through our bicycle model solution. This is to ensure that your trajectory is correct along with your model. The cell below will display the path generated by our model along with some waypoints on a desired figure 8. Surrounding these waypoints are error tolerance circles with radius 1.5m, your solution will pass the grader if the trajectory generated stays within 80% of these circles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Assessment passed! Your trajectory meets 90.0% of the waypoints.\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "grade_bicycle(t_data,v_data,w_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "The cell below will save the time and vehicle inputs as text file named $\\textit{figure8.txt}$. To locate the file, change the end of your web directory to $\\textit{/notebooks/Course_1_Module_4/figure8.txt}$\n",
    "\n",
    "Once you are there, you can download the file and submit to the Coursera grader to complete this assessment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = np.vstack([t_data, v_data, w_data]).T\n",
    "np.savetxt('figure8.txt', data, delimiter=', ')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Congratulations! You have now completed the assessment! Feel free to test the bicycle model with different inputs in the cell below, and see what trajectories they form. For example, try moving in an equilateral triangle. You'll find that it's rather difficult to generate desired trajectories by pre-setting the inputs. The next module on vehicle control will show you an easier and more accurate method. See you there!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample_time = 0.01\n",
    "time_end = 30\n",
    "model.reset()\n",
    "\n",
    "t_data = np.arange(0,time_end,sample_time)\n",
    "x_data = np.zeros_like(t_data)\n",
    "y_data = np.zeros_like(t_data)\n",
    "v_data = np.zeros_like(t_data)\n",
    "w_data = np.zeros_like(t_data)\n",
    "\n",
    "# ==================================\n",
    "#  Test various inputs here\n",
    "# ==================================\n",
    "for i in range(t_data.shape[0]):\n",
    "    model.step(v_data[i], w_data[i])\n",
    "    \n",
    "plt.axis('equal')\n",
    "plt.plot(x_data, y_data)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
